question
stringlengths 32
985
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stringlengths 1
13
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2.06k
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Bill buys 3 shirts for $25 each and 2 pairs of trousers for $50 each. He also buys a jacket for $100. He gets a 20% discount on the total. How much does he pay?
|
220
|
Step 1: Calculate the cost of the shirts.
Bill buys 3 shirts at $25 each.
$ 3 \times 25 = 75 $
So, the cost of the shirts is $75.
Step 2: Calculate the cost of the trousers.
Bill buys 2 pairs of trousers at $50 each.
$ 2 \times 50 = 100 $
So, the cost of the trousers is $100.
Step 3: Add the cost of the jacket.
The jacket costs $100.
Step 4: Calculate the total cost before the discount.
$ 75 + 100 + 100 = 275 $
So, the total cost before the discount is $275.
Step 5: Apply the 20% discount.
A 20% discount means Bill pays 80% of the total.
$ 275 \times 0.80 = 220 $
Bill pays $\boxed{220}$.
|
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] |
A library has 15 shelves and each shelf can accommodate 20 books. How many books can the library accommodate in total?
|
300
|
To find the total number of books the library can accommodate, we need to multiply the number of shelves by the number of books each shelf can hold.
Step 1: Identify the number of shelves, which is 15.
Step 2: Identify the number of books each shelf can hold, which is 20.
Step 3: Multiply the number of shelves by the number of books per shelf:
$$
15 \times 20 = 300
$$
The library can accommodate $\boxed{300}$ books in total.
|
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] |
A stadium contains 200 seats. Each row has 10 seats. Typically, only 1/5 of the seats are left unfilled. How many seats are usually occupied?
|
160
|
The stadium has a total of 200 seats.
We are told that only $ \frac{1}{5} $ of the seats are left unfilled. This means that $ \frac{4}{5} $ of the seats are usually occupied.
So, the number of seats usually occupied is:
$$
\frac{4}{5} \times 200 = 160
$$
$$
\boxed{160}
$$
|
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"path": "So, the number of seats usually occupied is:",
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{
"path": "So, the number of seats usually occupied is:",
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"path": "Now calculate the number of seats that are usually occupied:",
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{
"path": "Now calculate the number of occupied seats:",
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1
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{
"path": "Now, calculate the number of occupied seats:",
"score": 1,
"scores": [
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1,
1
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"is_final_answer": false
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{
"path": "So, we calculate:",
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{
"path": "Now calculate the number of occupied seats:",
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1,
1,
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"path": "So, the number of seats usually occupied is:",
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1,
1
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{
"path": "So, the number of seats usually occupied is:",
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1,
1
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{
"path": "So, the number of seats usually occupied is:",
"score": 1,
"scores": [
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1
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{
"path": "We calculate the number of occupied seats as follows:",
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1
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{
"path": "So, the number of seats usually occupied is:",
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"path": "Typically, only $ \\frac{1}{5} $ of the seats are left unfilled, meaning $ \\frac{4}{5} $ of the seats are occupied.",
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1,
1
],
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"path": "We are told that only 1/5 of the seats are left unfilled, meaning 4/5 of the seats are usually occupied.",
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"path": "Typically, only $ \\frac{1}{5} $ of the seats are left **unfilled**, which means $ \\frac{4}{5} $ of the seats are **occupied**.",
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] |
A train running at the speed of 60 kilometers per hour travels over a distance of 100 kilometers. How many hours did the journey take?
|
1.67
|
To find the time taken for the journey, we use the formula:
$$
\text{Time} = \frac{\text{Distance}}{\text{Speed}}
$$
Given:
- Distance = 100 kilometers
- Speed = 60 kilometers per hour
Substitute the values into the formula:
$$
\text{Time} = \frac{100}{60} = \frac{5}{3} \approx 1.67 \text{ hours}
$$
$$
\boxed{1.67}
$$
|
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New chefs have to buy cooking knives at the full price of $200, but chefs who have worked at least two years get a 15% discount. Chefs who have worked at least five years get an additional 10% off the discounted price. How much does a chef who has worked at least five years have to pay for the knives?
|
153
|
The original price of the knives is $200.
Step 1: Apply the 15% discount for chefs with at least two years of experience.
$$
15\% \text{ of } 200 = 0.15 \times 200 = 30
$$
$$
200 - 30 = 170
$$
So, after the 15% discount, the price is $170.
Step 2: Apply the additional 10% discount for chefs with at least five years of experience.
$$
10\% \text{ of } 170 = 0.10 \times 170 = 17
$$
$$
170 - 17 = 153
$$
A chef who has worked at least five years has to pay $\boxed{153}$ for the knives.
|
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Angie is preparing sandwiches for a picnic. She puts 3 slices of ham and 4 slices of cheese in each sandwich. If she is preparing 15 sandwiches, how many slices of ham and cheese does she need in total?
|
105
|
Step 1: Calculate the total number of ham slices needed.
Angie uses 3 slices of ham per sandwich, and she is making 15 sandwiches.
So, $ 3 \times 15 = 45 $ slices of ham are needed.
Step 2: Calculate the total number of cheese slices needed.
Angie uses 4 slices of cheese per sandwich, and she is making 15 sandwiches.
So, $ 4 \times 15 = 60 $ slices of cheese are needed.
Step 3: Add the total number of ham and cheese slices together.
$ 45 + 60 = 105 $
The total number of slices of ham and cheese Angie needs is $\boxed{105}$.
|
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"path": "Step 1: Calculate the total number of ham slices needed. \nEach sandwich uses 3 slices of ham, and there are 15 sandwiches. \n$$\n3 \\times 15 = 45 \\text{ slices of ham}\n$$",
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] |
John wants to buy a new phone which costs $800. He saves $100 each month. However, he already has $200 saved. How many months will it take for John to buy this phone?
|
6
|
John wants to buy a phone that costs $800. He already has $200 saved.
So, the remaining amount he needs is:
$800 - $200 = $600.
John saves $100 each month. To find out how many months it will take him to save the remaining $600, we divide:
$600 ÷ $100 = 6.
It will take John $\boxed{6}$ months to save enough to buy the phone.
|
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] |
Alex has a bag of marbles. He has 15 red marbles, twice that number of blue marbles, and half that number of green marbles. How many marbles does Alex have in total?
|
60
|
Alex has 15 red marbles.
He has twice that number of blue marbles, so:
$$
2 \times 15 = 30 \text{ blue marbles}
$$
He has half that number of green marbles, so:
$$
\frac{30}{2} = 15 \text{ green marbles}
$$
Now, we add all the marbles together:
$$
15 \text{ (red)} + 30 \text{ (blue)} + 15 \text{ (green)} = 60 \text{ marbles}
$$
$$
\boxed{60}
$$
|
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1
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{
"path": "The number of blue marbles is twice the number of red marbles: \n$ 2 \\times 15 = 30 $ blue marbles.",
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1,
1
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{
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"path": "He has half that number of green marbles: \n$ \\frac{1}{2} \\times 15 = 7.5 $, but since we can't have half a marble, we assume the number of green marbles is half of 15, which is 7 or 8. However, the question says \"half that number of green marbles,\" referring to the red marbles (15), so the green marbles are $ \\frac{1}{2} \\times 15 = 7.5 $. Since this is not a whole number, we may assume that the green marbles are 7 or that the problem expects rounding or fractional interpretation.",
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"path": "Now, add all the marbles together:\n$$\n15 \\text{ (red)} + 30 \\text{ (blue)} + 15 \\text{ (green)} = 60 \\text{ marbles}\n$$",
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"path": "Now, add all the marbles together:\n$$\n15 \\text{ (red)} + 30 \\text{ (blue)} + 15 \\text{ (green)} = 60 \\text{ marbles}\n$$",
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"path": "Now, we add all the marbles together:\n$$\n15 \\text{ (red)} + 30 \\text{ (blue)} + 15 \\text{ (green)} = 60 \\text{ marbles}\n$$",
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0.98828125
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{
"path": "Now, we add all the marbles together: \n$ 15 $ (red) $ + 30 $ (blue) $ + 15 $ (green) $ = 60 $.",
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0.345703125,
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"path": "Now, we add all the marbles together: \n$ 15 + 30 + 15 = 60 $",
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"scores": [
1,
1,
0.345703125,
0.98828125
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{
"path": "Now, we add all the marbles together: \n$ 15 + 30 + 15 = 60 $",
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0.345703125,
0.98828125
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{
"path": "Now, add all the marbles together: \n$ 15 + 30 + 15 = 60 $",
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{
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{
"path": "Now, add all the marbles together: \n$ 15 + 30 + 15 = 60 $",
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"path": "Let's clarify: if he has half the number of **blue** marbles in green marbles, then: \n$ \\frac{30}{2} = 15 $ green marbles.",
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"path": "Let’s re-express: \nAlex has 15 red marbles. \nHe has twice that number of blue marbles: \n$ 2 \\times 15 = 30 $ blue marbles. \nHe has half the number of blue marbles in green marbles: \n$ \\frac{30}{2} = 15 $ green marbles.",
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"path": "If the original statement is meant to be interpreted as \"half that number of red marbles,\" then we should use 15 as the base. However, \"half that number\" could ambiguously refer to the previous number (blue marbles). Let's clarify both interpretations.",
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"path": "Reinterpreting: \"half that number of green marbles\" likely refers to half the number of blue marbles, since blue is the most recent number mentioned.",
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] |
A hardware store is filling up its inventory. The screwdriver rack, which can hold 20 screwdrivers, currently has 7. The hammer rack, which can hold 15 hammers, currently has 9. The supplier charges $9 per screwdriver and $15 per hammer. How much, in dollars, will the store need to spend to fill the racks?
|
207
|
To determine how much the store needs to spend to fill the racks, we will calculate the number of additional tools needed for each rack and then multiply by their respective prices.
**Step 1: Calculate the number of additional screwdrivers needed.**
The rack can hold 20 screwdrivers, and there are currently 7.
So, the store needs:
$$
20 - 7 = 13 \text{ more screwdrivers}
$$
**Step 2: Calculate the cost of the additional screwdrivers.**
Each screwdriver costs $9, so:
$$
13 \times 9 = 117 \text{ dollars}
$$
**Step 3: Calculate the number of additional hammers needed.**
The rack can hold 15 hammers, and there are currently 9.
So, the store needs:
$$
15 - 9 = 6 \text{ more hammers}
$$
**Step 4: Calculate the cost of the additional hammers.**
Each hammer costs $15, so:
$$
6 \times 15 = 90 \text{ dollars}
$$
**Step 5: Add the costs together.**
$$
117 + 90 = 207
$$
The store will need to spend $\boxed{207}$ dollars to fill the racks.
|
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{
"path": "### Step 1: Calculate the number of additional screwdrivers needed\nThe screwdriver rack can hold 20 screwdrivers, and currently has 7.",
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"path": "Step 1: Calculate the number of additional screwdrivers needed. \nThe rack can hold 20 screwdrivers, and it currently has 7. \nSo, the store needs: \n$$ 20 - 7 = 13 $$ \nscrewdrivers.",
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"scores": [
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"path": "Step 1: Calculate the number of additional screwdrivers needed. \nThe rack can hold 20 screwdrivers and currently has 7. \nSo, the number of additional screwdrivers needed is: \n$ 20 - 7 = 13 $",
"score": 1,
"scores": [
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{
"path": "**Step 1: Calculate the number of screwdrivers needed** \nThe rack can hold 20 screwdrivers, and there are currently 7. \nSo, the number of screwdrivers needed is: \n$$\n20 - 7 = 13\n$$",
"score": 1,
"scores": [
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{
"path": "**Step 1: Calculate the number of screwdrivers needed.** \nThe rack can hold 20 screwdrivers and currently has 7. \nSo, the number of screwdrivers needed is: \n$$ 20 - 7 = 13 $$",
"score": 1,
"scores": [
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{
"path": "### Step 1: Calculate how many more screwdrivers are needed\nThe screwdriver rack can hold 20 screwdrivers, and it currently has 7.",
"score": 1,
"scores": [
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"is_final_answer": false
},
{
"path": "**Step 1: Calculate the number of screwdrivers needed.** \nThe rack can hold 20 screwdrivers, and it currently has 7. \n$$ 20 - 7 = 13 $$ \nSo, the store needs 13 more screwdrivers.",
"score": 1,
"scores": [
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],
"is_final_answer": false
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{
"path": "Step 1: Calculate the number of additional screwdrivers needed. \nThe screwdriver rack can hold 20 screwdrivers and currently has 7. \nSo, $ 20 - 7 = 13 $ screwdrivers are needed.",
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"scores": [
1,
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{
"path": "**Step 1: Calculate the number of screwdrivers needed** \nThe screwdriver rack can hold 20 screwdrivers and currently has 7. \nSo, the number of screwdrivers needed is: \n$$\n20 - 7 = 13\n$$",
"score": 1,
"scores": [
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{
"path": "**Step 1: Calculate the number of additional screwdrivers needed.** \nThe screwdriver rack can hold 20 screwdrivers and currently has 7. \nSo, the number of additional screwdrivers needed is: \n20 - 7 = 13",
"score": 1,
"scores": [
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{
"path": "**Step 1: Calculate the number of additional screwdrivers needed.** \nThe rack can hold 20 screwdrivers and currently has 7. \nSo, the number of additional screwdrivers needed is: \n$$ 20 - 7 = 13 $$",
"score": 1,
"scores": [
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"is_final_answer": false
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{
"path": "Step 1: Calculate the number of additional screwdrivers needed. \nThe screwdriver rack can hold 20 screwdrivers and currently has 7. \n$$ 20 - 7 = 13 $$ \nSo, the store needs 13 more screwdrivers.",
"score": 1,
"scores": [
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{
"path": "Step 1: Calculate the number of additional screwdrivers needed. \nThe rack can hold 20 screwdrivers and currently has 7. \n$$\n20 - 7 = 13 \\text{ screwdrivers}\n$$",
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"scores": [
1,
1
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},
{
"path": "**Step 1: Calculate the number of additional screwdrivers needed.** \nThe screwdriver rack can hold 20 screwdrivers, and it currently has 7. \nSo, the number of additional screwdrivers needed is: \n$$ 20 - 7 = 13 $$",
"score": 1,
"scores": [
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},
{
"path": "### Step 1: Calculate the number of screwdrivers needed\nThe screwdriver rack can hold 20 screwdrivers and currently has 7. So, the store needs:",
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"scores": [
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"depth": 2,
"candidates": [
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"path": "**Step 2: Calculate the cost of the additional screwdrivers.** \nEach screwdriver costs $9, so: \n$$\n13 \\times 9 = 117 \\text{ dollars}\n$$",
"score": 1,
"scores": [
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"is_final_answer": false
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{
"path": "**Step 2: Calculate the cost for the additional screwdrivers.** \nEach screwdriver costs $9, so the cost for 13 screwdrivers is: \n$$\n13 \\times 9 = 117 \\text{ dollars}\n$$",
"score": 1,
"scores": [
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{
"path": "**Step 2: Calculate the cost of the additional screwdrivers.** \nEach screwdriver costs $9, so the cost is: \n$$\n13 \\times 9 = 117 \\text{ dollars}\n$$",
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{
"path": "**Step 2: Calculate the cost for the additional screwdrivers.** \nEach screwdriver costs $9. \n$$\n13 \\times 9 = 117 \\text{ dollars}\n$$",
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"path": "$$\n20 - 7 = 13 \\text{ additional screwdrivers needed}\n$$",
"score": 1,
"scores": [
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"path": "$$\n20 - 7 = 13 \\text{ screwdrivers needed}\n$$",
"score": 1,
"scores": [
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"path": "$$\n20 - 7 = 13 \\text{ additional screwdrivers needed}\n$$",
"score": 1,
"scores": [
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"path": "$$\n20 - 7 = 13 \\text{ additional screwdrivers}\n$$",
"score": 1,
"scores": [
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],
"is_final_answer": false
},
{
"path": "Step 2: Calculate the number of additional hammers needed. \nThe rack can hold 15 hammers, and it currently has 9. \nSo, the store needs: \n$$ 15 - 9 = 6 $$ \nhammers.",
"score": 1,
"scores": [
1,
1,
1
],
"is_final_answer": false
},
{
"path": "Step 2: Calculate the number of additional hammers needed. \nThe rack can hold 15 hammers, and it currently has 9. \nSo, the store needs: \n$$ 15 - 9 = 6 $$ \nhammers.",
"score": 1,
"scores": [
1,
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],
"is_final_answer": false
},
{
"path": "Step 2: Calculate the number of additional hammers needed. \nThe rack can hold 15 hammers, and it currently has 9. \nSo, the store needs: \n$$ 15 - 9 = 6 $$ \nhammers.",
"score": 1,
"scores": [
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],
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},
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"path": "Step 2: Calculate the cost for the screwdrivers. \nEach screwdriver costs $9. \nSo, the cost for 13 screwdrivers is: \n$$ 13 \\times 9 = 117 $$ \ndollars.",
"score": 1,
"scores": [
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],
"is_final_answer": false
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"path": "Step 2: Calculate the cost of the additional screwdrivers. \nEach screwdriver costs $9. \nSo, the cost for 13 screwdrivers is: \n$ 13 \\times 9 = 117 $",
"score": 1,
"scores": [
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],
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"path": "Step 2: Calculate the cost for the additional screwdrivers. \nEach screwdriver costs $9. \nSo, the total cost for screwdrivers is: \n$ 13 \\times 9 = 117 $",
"score": 1,
"scores": [
1,
1,
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],
"is_final_answer": false
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{
"path": "Step 2: Calculate the cost for the additional screwdrivers. \nThe cost per screwdriver is $9. \nSo, the total cost for 13 screwdrivers is: \n$ 13 \\times 9 = 117 $",
"score": 1,
"scores": [
1,
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],
"is_final_answer": false
},
{
"path": "Step 2: Calculate the cost of the additional screwdrivers. \nEach screwdriver costs $9. \nSo, the total cost for screwdrivers is: \n$ 13 \\times 9 = 117 $",
"score": 1,
"scores": [
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],
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},
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"depth": 3,
"candidates": [
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"path": "**Step 3: Calculate the number of additional hammers needed.** \nThe rack can hold 15 hammers, and there are currently 9. \nSo, the store needs: \n$$\n15 - 9 = 6 \\text{ more hammers}\n$$",
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"scores": [
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"path": "**Step 3: Calculate the number of additional hammers needed.** \nThe rack can hold 15 hammers, and there are currently 9. \nSo, the store needs: \n$$\n15 - 9 = 6 \\text{ more hammers}\n$$",
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"path": "**Step 3: Calculate the number of additional hammers needed.** \nThe rack can hold 15 hammers, and there are currently 9. \nSo, the store needs: \n$$\n15 - 9 = 6 \\text{ more hammers}\n$$",
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"path": "**Step 3: Calculate the number of additional hammers needed.** \nThe rack can hold 15 hammers, and there are currently 9. \nSo, the store needs: \n$$\n15 - 9 = 6 \\text{ more hammers}\n$$",
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"path": "**Step 3: Calculate the number of additional hammers needed.** \nThe rack can hold 15 hammers, and there are currently 9. \nSo, the store needs: \n$$\n15 - 9 = 6 \\text{ more hammers}\n$$",
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"path": "**Step 3: Calculate the number of additional hammers needed.** \nThe rack can hold 15 hammers, and there are currently 9. \nSo, the store needs: \n$$\n15 - 9 = 6 \\text{ more hammers}\n$$",
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"path": "**Step 3: Calculate the number of additional hammers needed.** \nThe rack can hold 15 hammers, and there are currently 9. \nSo, the store needs: \n$$\n15 - 9 = 6 \\text{ more hammers}\n$$",
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"path": "**Step 3: Calculate the number of additional hammers needed.** \nThe rack can hold 15 hammers, and there are currently 9. \nSo, the store needs: \n$$\n15 - 9 = 6 \\text{ more hammers}\n$$",
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"path": "**Step 3: Calculate the number of additional hammers needed.** \nThe rack can hold 15 hammers, and there are currently 9. \nSo, the store needs: \n$$\n15 - 9 = 6 \\text{ more hammers}\n$$",
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"path": "**Step 3: Calculate the number of additional hammers needed.** \nThe rack can hold 15 hammers, and there are currently 9. \nSo, the store needs: \n$$\n15 - 9 = 6 \\text{ more hammers}\n$$",
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"path": "**Step 3: Calculate the number of additional hammers needed.** \nThe rack can hold 15 hammers, and there are currently 9. \nSo, the store needs: \n$$\n15 - 9 = 6 \\text{ more hammers}\n$$",
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"path": "**Step 3: Calculate the number of additional hammers needed.** \nThe rack can hold 15 hammers, and there are currently 9. \nSo, the store needs: \n$$\n15 - 9 = 6 \\text{ more hammers}\n$$",
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"path": "**Step 3: Calculate the number of additional hammers needed.** \nThe rack can hold 15 hammers, and there are currently 9. \nSo, the store needs: \n$$\n15 - 9 = 6 \\text{ more hammers}\n$$",
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"path": "**Step 3: Calculate the number of additional hammers needed.** \nThe rack can hold 15 hammers, and there are currently 9. \nSo, the store needs: \n$$\n15 - 9 = 6 \\text{ more hammers}\n$$",
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"path": "**Step 3: Calculate the number of additional hammers needed.** \nThe rack can hold 15 hammers, and there are currently 9. \nSo, the store needs: \n$$\n15 - 9 = 6 \\text{ more hammers}\n$$",
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"path": "**Step 3: Calculate the number of additional hammers needed.** \nThe rack can hold 15 hammers, and there are currently 9. \nSo, the store needs: \n$$\n15 - 9 = 6 \\text{ more hammers}\n$$",
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"depth": 4,
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"path": "**Step 4: Calculate the cost of the additional hammers.** \nEach hammer costs $15, so: \n$$\n6 \\times 15 = 90 \\text{ dollars}\n$$",
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"path": "**Step 4: Calculate the cost of the additional hammers.** \nEach hammer costs $15, so: \n$$\n6 \\times 15 = 90 \\text{ dollars}\n$$",
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"path": "**Step 4: Calculate the cost of the additional hammers.** \nEach hammer costs $15, so: \n$$\n6 \\times 15 = 90 \\text{ dollars}\n$$",
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"path": "**Step 4: Calculate the cost of the additional hammers.** \nEach hammer costs $15, so: \n$$\n6 \\times 15 = 90 \\text{ dollars}\n$$",
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"path": "**Step 4: Calculate the cost of the additional hammers.** \nEach hammer costs $15, so: \n$$\n6 \\times 15 = 90 \\text{ dollars}\n$$",
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"path": "**Step 4: Calculate the cost of the additional hammers.** \nEach hammer costs $15, so: \n$$\n6 \\times 15 = 90 \\text{ dollars}\n$$",
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"path": "**Step 4: Calculate the cost of the additional hammers.** \nEach hammer costs $15, so: \n$$\n6 \\times 15 = 90 \\text{ dollars}\n$$",
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"path": "**Step 4: Calculate the cost of the additional hammers.** \nEach hammer costs $15, so: \n$$\n6 \\times 15 = 90 \\text{ dollars}\n$$",
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"path": "**Step 4: Calculate the cost of the additional hammers.** \nEach hammer costs $15, so: \n$$\n6 \\times 15 = 90 \\text{ dollars}\n$$",
"score": 1,
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1,
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"path": "**Step 4: Calculate the cost of the additional hammers.** \nEach hammer costs $15, so: \n$$\n6 \\times 15 = 90 \\text{ dollars}\n$$",
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"path": "**Step 4: Calculate the cost of the additional hammers.** \nEach hammer costs $15, so: \n$$\n6 \\times 15 = 90 \\text{ dollars}\n$$",
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"path": "**Step 4: Calculate the cost of the additional hammers.** \nEach hammer costs $15, so: \n$$\n6 \\times 15 = 90 \\text{ dollars}\n$$",
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"path": "**Step 4: Calculate the cost of the additional hammers.** \nEach hammer costs $15, so: \n$$\n6 \\times 15 = 90 \\text{ dollars}\n$$",
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"path": "**Step 4: Calculate the cost of the additional hammers.** \nEach hammer costs $15, so: \n$$\n6 \\times 15 = 90 \\text{ dollars}\n$$",
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],
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"path": "**Step 4: Calculate the cost of the additional hammers.** \nEach hammer costs $15, so: \n$$\n6 \\times 15 = 90 \\text{ dollars}\n$$",
"score": 1,
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{
"path": "**Step 4: Calculate the cost of the additional hammers.** \nEach hammer costs $15, so: \n$$\n6 \\times 15 = 90 \\text{ dollars}\n$$",
"score": 1,
"scores": [
1,
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],
"is_final_answer": false
}
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},
{
"depth": 5,
"candidates": [
{
"path": "**Step 5: Add the costs together.** \n$$\n117 + 90 = 207\n$$",
"score": 1,
"scores": [
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],
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},
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"path": "**Step 5: Add the total costs together.** \n$$\n117 + 90 = 207\n$$",
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"path": "**Step 5: Add the costs for screwdrivers and hammers.** \n$$\n117 + 90 = 207 \\text{ dollars}\n$$",
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"path": "**Step 5: Add the costs together to find the total amount the store needs to spend.** \n$$\n117 + 90 = 207\n$$",
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"path": "**Step 5: Add the costs together.** \n$$\n117 + 90 = 207\n$$",
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"path": "**Step 5: Add the costs together.** \n$$\n117 + 90 = 207\n$$",
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"path": "**Step 5: Add the costs together to find the total cost.** \n$$\n117 + 90 = 207\n$$",
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"path": "**Step 5: Add the costs together to find the total.** \n$$\n117 + 90 = 207\n$$",
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"path": "**Step 5: Add the costs together.** \n$$\n117 + 90 = 207\n$$",
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"path": "**Step 5: Add the costs together.** \n$$\n117 + 90 = 207\n$$",
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"path": "**Step 5: Calculate the total cost.** \n$$\n117 + 90 = 207 \\text{ dollars}\n$$",
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"path": "**Step 5: Add the costs of screwdrivers and hammers.** \n$$\n117 + 90 = 207\n$$",
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"path": "**Step 5: Add the costs for both tools.** \n$$\n117 + 90 = 207\n$$",
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},
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"depth": 6,
"candidates": [
{
"path": "The store will need to spend $\\boxed{207}$ dollars to fill the racks.",
"score": 1,
"scores": [
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],
"is_final_answer": true
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"path": "The store will need to spend $\\boxed{207}$ dollars to fill the racks.",
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"score": 1,
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"path": "The store will need to spend $\\boxed{207}$ dollars to fill the racks.",
"score": 1,
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] |
Rachel makes a 4-page journal to 3 different friends every month. How many pages does she make in a year?
|
144
|
Rachel makes a 4-page journal for each of her 3 friends every month.
Step 1: Calculate the total number of pages Rachel makes each month.
She makes 4 pages per friend, and she has 3 friends:
$$ 4 \times 3 = 12 \text{ pages per month} $$
Step 2: Calculate the total number of pages in a year.
There are 12 months in a year:
$$ 12 \times 12 = 144 \text{ pages per year} $$
$$
\boxed{144}
$$
|
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] |
Ali has three times as many soccer balls as Bruno. If Bruno has 5 soccer balls, how many soccer balls would they have in total if they put their balls together?
|
20
|
Bruno has 5 soccer balls.
Ali has three times as many soccer balls as Bruno, so Ali has $ 3 \times 5 = 15 $ soccer balls.
Adding their soccer balls together:
$ 5 + 15 = 20 $
\boxed{20}
|
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"is_final_answer": false
},
{
"path": "$$\n3 \\times 5 = 15\n$$",
"score": 0.98046875,
"scores": [
0.9609375,
1
],
"is_final_answer": false
}
]
},
{
"depth": 2,
"candidates": [
{
"path": "The total number of soccer balls they have together is $\\boxed{20}$.",
"score": 0.9986979166666666,
"scores": [
0.99609375,
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1
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"is_final_answer": true
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{
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{
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{
"path": "$$\n\\boxed{20}\n$$",
"score": 0.9973958333333334,
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0.99609375,
0.99609375,
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},
{
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"score": 0.9973958333333334,
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0.99609375,
0.99609375,
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},
{
"path": "\\boxed{20}",
"score": 0.9973958333333334,
"scores": [
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0.99609375,
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},
{
"path": "\\boxed{20}",
"score": 0.9973958333333334,
"scores": [
0.99609375,
0.99609375,
1
],
"is_final_answer": true
},
{
"path": "\\boxed{20}",
"score": 0.9973958333333334,
"scores": [
0.99609375,
0.99609375,
1
],
"is_final_answer": true
}
]
}
] |
Kathy has an e-book which has 150 pages. She reads 10 pages a day. After 5 days, how many pages are left for Kathy to read?
|
100
|
Kathy reads 10 pages a day for 5 days.
So, the total number of pages she reads is:
10 pages/day × 5 days = 50 pages.
The e-book has 150 pages in total.
After reading 50 pages, the number of pages left is:
150 pages − 50 pages = 100 pages.
$$
\boxed{100}
$$
|
[
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{
"path": "Kathy reads 10 pages per day. \nOver 5 days, she reads: \n$ 10 \\times 5 = 50 $ pages.",
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"scores": [
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{
"path": "Kathy reads 10 pages a day for 5 days. \nSo, the total number of pages she reads is: \n10 pages/day × 5 days = 50 pages.",
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"scores": [
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{
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{
"path": "Kathy reads 10 pages per day. Over 5 days, she will have read:",
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{
"path": "Kathy reads 10 pages per day. Over 5 days, she will have read:",
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"scores": [
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{
"path": "Kathy reads 10 pages a day for 5 days. So, the total number of pages she has read is:",
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},
{
"path": "Kathy reads 10 pages per day. Over 5 days, she will read:",
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{
"path": "Kathy reads 10 pages a day. Over 5 days, she reads:",
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{
"path": "Kathy reads 10 pages a day. Over 5 days, she reads:",
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{
"path": "Kathy reads 10 pages each day. Over 5 days, she will read:",
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{
"path": "Kathy reads 10 pages per day. Over 5 days, she reads:",
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{
"path": "Kathy reads 10 pages per day. Over 5 days, she reads:",
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{
"path": "Kathy reads 10 pages per day. Over 5 days, she reads:",
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"path": "Kathy reads 10 pages per day. Over 5 days, she reads:",
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"path": "Kathy reads 10 pages per day. Over 5 days, she reads:",
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{
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{
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{
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"scores": [
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{
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"scores": [
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{
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{
"path": "The e-book has 150 pages in total. \nAfter reading 50 pages, the number of pages left is: \n$ 150 - 50 = 100 $.",
"score": 0.99609375,
"scores": [
0.99609375,
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{
"path": "The e-book has 150 pages in total. \nAfter reading 50 pages, the number of pages left is: \n$ 150 - 50 = 100 $.",
"score": 0.99609375,
"scores": [
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0.99609375
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"path": "The e-book has 150 pages in total. \nSubtracting the pages she has read: \n150 pages − 50 pages = 100 pages.",
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"scores": [
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"path": "The e-book has 150 pages in total. \nSubtracting the pages she has already read: \n150 pages − 50 pages = 100 pages.",
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"scores": [
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{
"path": "The e-book has 150 pages in total. \nSo, the number of pages left for Kathy to read is $ 150 - 50 = 100 $.",
"score": 0.99609375,
"scores": [
0.99609375,
0.99609375
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},
{
"path": "$$\n10 \\text{ pages/day} \\times 5 \\text{ days} = 50 \\text{ pages}\n$$",
"score": 0.990234375,
"scores": [
0.98046875,
1
],
"is_final_answer": false
},
{
"path": "$$\n10 \\times 5 = 50 \\text{ pages}\n$$",
"score": 0.990234375,
"scores": [
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},
{
"path": "$$\n10 \\text{ pages/day} \\times 5 \\text{ days} = 50 \\text{ pages}\n$$",
"score": 0.990234375,
"scores": [
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}
]
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],
"is_final_answer": true
},
{
"path": "$$\n\\boxed{100}\n$$",
"score": 0.9986979166666666,
"scores": [
0.99609375,
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],
"is_final_answer": true
},
{
"path": "$$\n\\boxed{100}\n$$",
"score": 0.9986979166666666,
"scores": [
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],
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{
"path": "$$\n\\boxed{100}\n$$",
"score": 0.9986979166666666,
"scores": [
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],
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},
{
"path": "$$\n\\boxed{100}\n$$",
"score": 0.9986979166666666,
"scores": [
0.99609375,
1,
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],
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},
{
"path": "\\boxed{100}",
"score": 0.9986979166666666,
"scores": [
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1,
1
],
"is_final_answer": true
},
{
"path": "$$\n\\boxed{100}\n$$",
"score": 0.9986979166666666,
"scores": [
0.99609375,
1,
1
],
"is_final_answer": true
},
{
"path": "\\boxed{100}",
"score": 0.9986979166666666,
"scores": [
0.99609375,
1,
1
],
"is_final_answer": true
},
{
"path": "$$\n\\boxed{100}\n$$",
"score": 0.9986979166666666,
"scores": [
0.99609375,
1,
1
],
"is_final_answer": true
},
{
"path": "$$\n\\boxed{100}\n$$",
"score": 0.9986979166666666,
"scores": [
0.99609375,
1,
1
],
"is_final_answer": true
},
{
"path": "$$\n\\boxed{100}\n$$",
"score": 0.9986979166666666,
"scores": [
0.99609375,
1,
1
],
"is_final_answer": true
},
{
"path": "$$\n\\boxed{100}\n$$",
"score": 0.9986979166666666,
"scores": [
0.99609375,
1,
1
],
"is_final_answer": true
},
{
"path": "$$\n\\boxed{100}\n$$",
"score": 0.9986979166666666,
"scores": [
0.99609375,
1,
1
],
"is_final_answer": true
},
{
"path": "\\boxed{100}",
"score": 0.9986979166666666,
"scores": [
0.99609375,
1,
1
],
"is_final_answer": true
},
{
"path": "\\boxed{100}",
"score": 0.9986979166666666,
"scores": [
0.99609375,
1,
1
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},
{
"path": "$$\n\\boxed{100}\n$$",
"score": 0.9986979166666666,
"scores": [
0.99609375,
1,
1
],
"is_final_answer": true
}
]
}
] |
Alex currently has 40 stamps, but he used to have more. Alex gave his cousin 80 stamps, gave his brother twice that amount and gave his friend Christopher three times the amount he currently has. How many stamps did Alex start with?
|
400
|
Let's denote the number of stamps Alex originally had as $ x $.
We are told the following:
- Alex currently has 40 stamps.
- He gave his cousin 80 stamps.
- He gave his brother twice that amount, which is $ 2 \times 80 = 160 $ stamps.
- He gave his friend Christopher three times the amount he currently has, which is $ 3 \times 40 = 120 $ stamps.
Now, let's calculate the total number of stamps Alex gave away:
$$
80 + 160 + 120 = 360
$$
This means Alex gave away a total of 360 stamps. Since he currently has 40 stamps, the total number of stamps he started with is:
$$
x = 360 + 40 = 400
$$
$$
\boxed{400}
$$
|
[
{
"depth": 0,
"candidates": [
{
"path": "Let's denote the number of stamps Alex originally had as $ x $.",
"score": 1,
"scores": [
1
],
"is_final_answer": false
},
{
"path": "Let's define the problem step by step.",
"score": 1,
"scores": [
1
],
"is_final_answer": false
},
{
"path": "Let's break down the problem step by step.",
"score": 1,
"scores": [
1
],
"is_final_answer": false
},
{
"path": "Let's break down the problem step by step.",
"score": 1,
"scores": [
1
],
"is_final_answer": false
},
{
"path": "Alex currently has 40 stamps. Let's denote the number of stamps Alex originally had as $ x $.",
"score": 1,
"scores": [
1
],
"is_final_answer": false
},
{
"path": "Let’s define the number of stamps Alex originally had as $ x $.",
"score": 1,
"scores": [
1
],
"is_final_answer": false
},
{
"path": "Let's break down the problem step by step.",
"score": 1,
"scores": [
1
],
"is_final_answer": false
},
{
"path": "Let's define the unknown quantity and work through the problem step by step.",
"score": 1,
"scores": [
1
],
"is_final_answer": false
},
{
"path": "Let's break the problem down step by step.",
"score": 1,
"scores": [
1
],
"is_final_answer": false
},
{
"path": "Alex currently has 40 stamps, but he gave away a total of some stamps before ending up with this amount. Let's figure out how many he gave away and work backwards to find out how many he started with.",
"score": 0.99609375,
"scores": [
0.99609375
],
"is_final_answer": false
},
{
"path": "Alex currently has 40 stamps. Let's work through the problem step by step.",
"score": 0.99609375,
"scores": [
0.99609375
],
"is_final_answer": false
},
{
"path": "Alex currently has 40 stamps, but he gave away several amounts before that. Let's track the total number of stamps he gave away and then work backward to find out how many stamps he originally had.",
"score": 0.99609375,
"scores": [
0.99609375
],
"is_final_answer": false
},
{
"path": "Alex currently has 40 stamps. We are told that he gave away some stamps in the past, and we need to determine how many stamps he started with.",
"score": 0.99609375,
"scores": [
0.99609375
],
"is_final_answer": false
},
{
"path": "Let's define the variable:",
"score": 0.9921875,
"scores": [
0.9921875
],
"is_final_answer": false
},
{
"path": "Let's break the problem into steps:",
"score": 0.984375,
"scores": [
0.984375
],
"is_final_answer": false
},
{
"path": "Let's break the problem into steps:",
"score": 0.984375,
"scores": [
0.984375
],
"is_final_answer": false
}
]
},
{
"depth": 1,
"candidates": [
{
"path": "We are told the following:",
"score": 1,
"scores": [
1,
1
],
"is_final_answer": false
},
{
"path": "We are told that Alex currently has 40 stamps. However, he gave away some stamps in the past, and we are to find out how many stamps he started with.",
"score": 1,
"scores": [
1,
1
],
"is_final_answer": false
},
{
"path": "Let $ x $ be the number of stamps Alex originally had.",
"score": 1,
"scores": [
1,
1
],
"is_final_answer": false
},
{
"path": "We are told that Alex currently has **40 stamps**, but he used to have more. He gave away different amounts of stamps to his cousin, brother, and friend Christopher. We need to determine how many stamps Alex **originally had**.",
"score": 1,
"scores": [
1,
1
],
"is_final_answer": false
},
{
"path": "We are told that Alex currently has 40 stamps, but he used to have more. He gave away some stamps to his cousin, brother, and friend Christopher. We are to find out how many stamps Alex started with.",
"score": 1,
"scores": [
1,
1
],
"is_final_answer": false
},
{
"path": "We are told that Alex currently has 40 stamps, but he used to have more. We need to find out how many stamps he started with.",
"score": 1,
"scores": [
1,
1
],
"is_final_answer": false
},
{
"path": "We are told:",
"score": 0.998046875,
"scores": [
1,
0.99609375
],
"is_final_answer": false
},
{
"path": "We are told that Alex currently has 40 stamps. This means that after giving away some stamps, he is left with 40. Let's break down the information:",
"score": 0.998046875,
"scores": [
1,
0.99609375
],
"is_final_answer": false
},
{
"path": "We are told that Alex currently has 40 stamps, but he used to have more. He gave away some stamps:",
"score": 0.998046875,
"scores": [
1,
0.99609375
],
"is_final_answer": false
},
{
"path": "---",
"score": 0.998046875,
"scores": [
1,
0.99609375
],
"is_final_answer": false
},
{
"path": "We are told that:",
"score": 0.99609375,
"scores": [
1,
0.9921875
],
"is_final_answer": false
},
{
"path": "We are told that Alex currently has **40 stamps**, but he used to have more. He gave away some stamps in the following way:",
"score": 0.99609375,
"scores": [
1,
0.9921875
],
"is_final_answer": false
},
{
"path": "We are told that Alex currently has **40 stamps**. But he gave away some stamps before that. We need to find how many stamps Alex **started with** before giving any away.",
"score": 0.99609375,
"scores": [
1,
0.9921875
],
"is_final_answer": false
},
{
"path": "We are told that Alex currently has **40 stamps**, but he used to have more. We are also told how many stamps he gave away to different people:",
"score": 0.9921875,
"scores": [
1,
0.984375
],
"is_final_answer": false
},
{
"path": "We are told that Alex currently has 40 stamps, but he used to have more. He gave away:",
"score": 0.98828125,
"scores": [
1,
0.9765625
],
"is_final_answer": false
},
{
"path": "We are told that Alex currently has **40 stamps**, but he used to have more. He gave away stamps to three different people:",
"score": 0.986328125,
"scores": [
1,
0.97265625
],
"is_final_answer": false
}
]
},
{
"depth": 2,
"candidates": [
{
"path": "- Alex currently has 40 stamps.\n- He gave his cousin 80 stamps.\n- He gave his brother twice that amount, which is $ 2 \\times 80 = 160 $ stamps.\n- He gave his friend Christopher three times the amount he currently has, which is $ 3 \\times 40 = 120 $ stamps.",
"score": 1,
"scores": [
1,
1,
1
],
"is_final_answer": false
},
{
"path": "- Alex currently has **40 stamps**.\n- He **gave his cousin 80 stamps**.\n- He gave his **brother twice that amount**, which is $ 2 \\times 80 = 160 $ stamps.\n- He gave his **friend Christopher three times the amount he currently has**, which is $ 3 \\times 40 = 120 $ stamps.",
"score": 1,
"scores": [
1,
1,
1
],
"is_final_answer": false
},
{
"path": "- Alex currently has 40 stamps.\n- He gave his cousin 80 stamps.\n- He gave his brother twice that amount, which is $ 2 \\times 80 = 160 $ stamps.\n- He gave his friend Christopher three times the amount he currently has, which is $ 3 \\times 40 = 120 $ stamps.",
"score": 1,
"scores": [
1,
1,
1
],
"is_final_answer": false
},
{
"path": "Let’s call the number of stamps Alex started with $ x $.",
"score": 1,
"scores": [
1,
1,
1
],
"is_final_answer": false
},
{
"path": "Let’s denote the number of stamps Alex originally had as $ x $.",
"score": 1,
"scores": [
1,
1,
1
],
"is_final_answer": false
},
{
"path": "We are told that Alex currently has 40 stamps. That means he gave away some stamps, and what's left is 40.",
"score": 1,
"scores": [
1,
1,
1
],
"is_final_answer": false
},
{
"path": "---",
"score": 1,
"scores": [
1,
1,
1
],
"is_final_answer": false
},
{
"path": "---",
"score": 1,
"scores": [
1,
1,
1
],
"is_final_answer": false
},
{
"path": "---",
"score": 1,
"scores": [
1,
1,
1
],
"is_final_answer": false
},
{
"path": "---",
"score": 1,
"scores": [
1,
1,
1
],
"is_final_answer": false
},
{
"path": "- Alex currently has 40 stamps.\n- He gave his cousin 80 stamps.\n- He gave his brother **twice** that amount (i.e., $ 2 \\times 80 = 160 $ stamps).\n- He gave his friend Christopher **three times the amount he currently has**, which is $ 3 \\times 40 = 120 $ stamps.",
"score": 0.9986979166666666,
"scores": [
1,
1,
0.99609375
],
"is_final_answer": false
},
{
"path": "---",
"score": 0.9986979166666666,
"scores": [
1,
1,
0.99609375
],
"is_final_answer": false
},
{
"path": "---",
"score": 0.9986979166666666,
"scores": [
1,
1,
0.99609375
],
"is_final_answer": false
},
{
"path": "We are told that:",
"score": 0.9986979166666666,
"scores": [
1,
1,
0.99609375
],
"is_final_answer": false
},
{
"path": "We are told that:",
"score": 0.9986979166666666,
"scores": [
1,
1,
0.99609375
],
"is_final_answer": false
},
{
"path": "We are told that:",
"score": 0.9986979166666666,
"scores": [
1,
1,
0.99609375
],
"is_final_answer": false
}
]
},
{
"depth": 3,
"candidates": [
{
"path": "Now, let's calculate the total number of stamps Alex gave away:",
"score": 1,
"scores": [
1,
1,
1,
1
],
"is_final_answer": false
},
{
"path": "So, the total number of stamps Alex gave away is:\n$$\n80 + 160 + 120 = 360\n$$",
"score": 1,
"scores": [
1,
1,
1,
1
],
"is_final_answer": false
},
{
"path": "So, in total, Alex gave away:\n$$\n80 + 160 + 120 = 360 \\text{ stamps}\n$$",
"score": 1,
"scores": [
1,
1,
1,
1
],
"is_final_answer": false
},
{
"path": "So, the total number of stamps Alex gave away is:\n$$\n80 + 160 + 120 = 360\n$$",
"score": 1,
"scores": [
1,
1,
1,
1
],
"is_final_answer": false
},
{
"path": "Now, let's break down what happened:",
"score": 1,
"scores": [
1,
1,
1,
1
],
"is_final_answer": false
},
{
"path": "Now, let's break down what he gave away:",
"score": 1,
"scores": [
1,
1,
1,
1
],
"is_final_answer": false
},
{
"path": "Now, let's break down the stamps he gave away:",
"score": 1,
"scores": [
1,
1,
1,
1
],
"is_final_answer": false
},
{
"path": "Now, let's break down what he gave away:",
"score": 1,
"scores": [
1,
1,
1,
1
],
"is_final_answer": false
},
{
"path": "So, the total number of stamps Alex gave away is:",
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"scores": [
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1,
1,
0.99609375
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"is_final_answer": false
},
{
"path": "So, the total number of stamps Alex gave away is:",
"score": 0.9990234375,
"scores": [
1,
1,
1,
0.99609375
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"is_final_answer": false
},
{
"path": "So the total number of stamps Alex gave away is:",
"score": 0.9990234375,
"scores": [
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1,
1,
0.99609375
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"is_final_answer": false
},
{
"path": "So, the total number of stamps Alex gave away is:",
"score": 0.9990234375,
"scores": [
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1,
1,
0.99609375
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"is_final_answer": false
},
{
"path": "So the total number of stamps he gave away is:",
"score": 0.9990234375,
"scores": [
1,
1,
1,
0.99609375
],
"is_final_answer": false
},
{
"path": "So, the total number of stamps Alex gave away is:",
"score": 0.998046875,
"scores": [
1,
1,
1,
0.9921875
],
"is_final_answer": false
},
{
"path": "So, the total number of stamps Alex gave away is:",
"score": 0.998046875,
"scores": [
1,
1,
1,
0.9921875
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"is_final_answer": false
},
{
"path": "So, in total, Alex gave away:",
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0.984375
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"path": "$$\n80 + 160 + 120 = 360\n$$",
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{
"path": "$$\n80 + 160 + 120 = 360\n$$",
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1
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},
{
"path": "$$\n80 \\text{ (cousin)} + 160 \\text{ (brother)} + 120 \\text{ (Christopher)} = 360 \\text{ stamps}\n$$",
"score": 1,
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1,
1,
1,
1,
1
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{
"path": "$$\n80 + 160 + 120 = 360\n$$",
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1,
1
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{
"path": "Since Alex now has 40 stamps, the original number of stamps he had must be:\n$$\nx = 40 + 360 = 400\n$$",
"score": 1,
"scores": [
1,
1,
1,
1,
1
],
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},
{
"path": "Since Alex now has 40 stamps, that means the number of stamps he originally had is:\n$$\nx = 40 + 360 = 400\n$$",
"score": 1,
"scores": [
1,
1,
1,
1,
1
],
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},
{
"path": "If he currently has 40 stamps and gave away 360 stamps, the total number of stamps he originally had is:\n$$\nx = 40 + 360 = 400\n$$",
"score": 1,
"scores": [
1,
1,
1,
1,
1
],
"is_final_answer": false
},
{
"path": "We also know that Alex currently has 40 stamps, which means the original number of stamps minus the number he gave away equals the current number of stamps:\n$$\nx - 360 = 40\n$$",
"score": 1,
"scores": [
1,
1,
1,
1,
1
],
"is_final_answer": false
},
{
"path": "Since he currently has 40 stamps, that means he started with:\n$$\nx = 40 + 360 = 400\n$$",
"score": 1,
"scores": [
1,
1,
1,
1,
1
],
"is_final_answer": false
},
{
"path": "Since Alex currently has 40 stamps, the total number of stamps he originally had is the number of stamps he gave away plus the number of stamps he has now:\n$$\nx = 360 + 40 = 400\n$$",
"score": 1,
"scores": [
1,
1,
1,
1,
1
],
"is_final_answer": false
},
{
"path": "Since he currently has 40 stamps, the number of stamps he started with is:\n$$\nx = 40 + 360 = 400\n$$",
"score": 1,
"scores": [
1,
1,
1,
1,
1
],
"is_final_answer": false
},
{
"path": "Since Alex currently has 40 stamps, the total number of stamps he originally had is:\n$$\nx = 40 + 360 = 400\n$$",
"score": 1,
"scores": [
1,
1,
1,
1,
1
],
"is_final_answer": false
},
{
"path": "Since Alex now has 40 stamps left, the total number of stamps he originally had must be:\n$$\nx = 40 + 360 = 400\n$$",
"score": 1,
"scores": [
1,
1,
1,
1,
1
],
"is_final_answer": false
},
{
"path": "Since Alex now has 40 stamps, that means the total number of stamps he had originally was the number of stamps he gave away plus the number of stamps he has now:\n$$\nx = 360 + 40 = 400\n$$",
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0.99609375
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{
"path": "Since Alex now has 40 stamps, that means the original number of stamps he had was:\n$$\nx - 360 = 40\n$$",
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1,
1,
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1,
0.97265625
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{
"path": "Since Alex now has 40 stamps, that means he originally had:\n$$\nx - 360 = 40\n$$",
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1,
1,
0.9375
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"path": "So, Alex gave away 360 stamps in total.",
"score": 1,
"scores": [
1,
1,
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{
"path": "So Alex gave away a total of 360 stamps.",
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{
"path": "This means Alex gave away a total of 360 stamps. Since he currently has 40 stamps, the total number of stamps he started with is:",
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"path": "So, the total number of stamps Alex had originally is the number of stamps he gave away plus the number he currently has:",
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"path": "Since Alex currently has 40 stamps, the total number of stamps he originally had is the sum of the stamps he gave away and the stamps he has now:",
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0.99609375
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"path": "Since he currently has 40 stamps, the total number of stamps he originally had is the number of stamps he gave away plus the number of stamps he still has:",
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1,
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{
"path": "So, Alex gave away a total of 360 stamps. Since he currently has 40 stamps, the total number of stamps he originally had is:",
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"scores": [
1,
1,
1,
1,
1,
0.99609375
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{
"path": "This means Alex gave away a total of 360 stamps. Since he currently has 40 stamps, the total number of stamps he originally had must be:",
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"scores": [
1,
1,
1,
1,
1,
0.9921875
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"is_final_answer": false
},
{
"path": "Since Alex currently has 40 stamps left, the number of stamps he originally had is the amount he gave away plus the amount he currently has:",
"score": 0.9986979166666666,
"scores": [
1,
1,
1,
1,
1,
0.9921875
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{
"path": "Since Alex currently has 40 stamps, that means he originally had:",
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0.98828125
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"is_final_answer": false
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{
"path": "Since Alex currently has 40 stamps, and he gave away 360 stamps, the number of stamps he originally had is:",
"score": 0.998046875,
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1,
1,
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0.98828125
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{
"path": "Since Alex now has 40 stamps, and he gave away 360 stamps, the total number of stamps he originally had is:",
"score": 0.998046875,
"scores": [
1,
1,
1,
1,
1,
0.98828125
],
"is_final_answer": false
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{
"path": "So, Alex gave away a total of 360 stamps. Since he currently has 40 stamps, we can write:",
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"scores": [
1,
1,
1,
1,
1,
0.98828125
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"is_final_answer": false
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{
"path": "Since Alex now has 40 stamps left, we can find the original number of stamps by adding the 40 stamps he currently has to the 360 stamps he gave away:",
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"path": "So, Alex gave away a total of 360 stamps. Since he currently has 40 stamps left, the total number of stamps he originally had is:",
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"path": "Since Alex currently has 40 stamps, the total number of stamps he originally had must be:",
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0.9765625
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1,
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1,
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0.99609375
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0.99609375,
1
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0.99609375,
1
],
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{
"path": "$$\nx = 360 + 40 = 400\n$$",
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"scores": [
1,
1,
1,
1,
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0.99609375,
1
],
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},
{
"path": "Since he currently has 40 stamps, that means he must have had:",
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0.9921875
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"path": "Since he currently has 40 stamps, the number of stamps he originally had is:",
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0.9921875
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"path": "Since he currently has 40 stamps, the total number of stamps he originally had is:",
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1,
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0.9921875
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{
"path": "We also know that he currently has 40 stamps left. That means the total number of stamps he had originally is the sum of the stamps he gave away and the ones he has left:",
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1,
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0.98828125
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{
"path": "Since he currently has 40 stamps, and he gave away 360, we can set up the equation:",
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0.96875
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"path": "We are told that Alex currently has 40 stamps. That means:",
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0.953125
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1,
1,
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0.94921875
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"path": "$$\nx = 40 + 360 = 400\n$$",
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{
"path": "$$\n\\boxed{400}\n$$",
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0.99609375,
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},
{
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0.99609375,
1,
1
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{
"path": "$$\n\\boxed{400}\n$$",
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0.99609375,
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{
"path": "$$\n\\boxed{400}\n$$",
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0.99609375,
1,
1
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},
{
"path": "$$\n\\boxed{400}\n$$",
"score": 0.99951171875,
"scores": [
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1,
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1,
0.99609375,
1,
1
],
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},
{
"path": "$$\n\\boxed{400}\n$$",
"score": 0.99951171875,
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0.99609375,
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1
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},
{
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1,
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0.99609375,
1,
1
],
"is_final_answer": true
},
{
"path": "So, Alex started with $\\boxed{400}$ stamps.",
"score": 0.99951171875,
"scores": [
1,
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1,
1,
0.99609375,
1,
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{
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0.99609375,
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1
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{
"path": "$$\n\\boxed{400}\n$$",
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0.99609375,
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1
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},
{
"path": "$$\n\\boxed{400}\n$$",
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1,
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1,
1,
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0.99609375,
1,
1
],
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},
{
"path": "$$\nx - 360 = 40\n$$",
"score": 0.9892578125,
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1,
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0.99609375,
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"is_final_answer": false
}
]
}
] |
Olivia has 7 cats and 12 dogs. If she adopts 2 more dogs and buys 2 more cats, how many pets will she have in total?
|
23
|
Olivia currently has 7 cats and 12 dogs.
She adopts 2 more dogs, so the number of dogs becomes:
$$ 12 + 2 = 14 $$
She also buys 2 more cats, so the number of cats becomes:
$$ 7 + 2 = 9 $$
Now, we add the total number of pets:
$$ 14 + 9 = 23 $$
$$
\boxed{23}
$$
|
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{
"path": "Olivia currently has 7 cats and 12 dogs.",
"score": 1,
"scores": [
1
],
"is_final_answer": false
},
{
"path": "Olivia currently has 7 cats and 12 dogs. \nShe adopts 2 more dogs and buys 2 more cats.",
"score": 0.99609375,
"scores": [
0.99609375
],
"is_final_answer": false
},
{
"path": "Olivia currently has 7 cats and 12 dogs. \nShe adopts 2 more dogs, so the number of dogs becomes $12 + 2 = 14$. \nShe buys 2 more cats, so the number of cats becomes $7 + 2 = 9$.",
"score": 0.9921875,
"scores": [
0.9921875
],
"is_final_answer": false
},
{
"path": "Olivia initially has 7 cats and 12 dogs. \nSo, the total number of pets she has initially is: \n7 (cats) + 12 (dogs) = 19 pets.",
"score": 0.9765625,
"scores": [
0.9765625
],
"is_final_answer": false
},
{
"path": "Olivia initially has 7 cats and 12 dogs. \nSo, the total number of pets she has at the beginning is: \n7 (cats) + 12 (dogs) = 19 pets.",
"score": 0.97265625,
"scores": [
0.97265625
],
"is_final_answer": false
},
{
"path": "Olivia initially has 7 cats and 12 dogs. \nSo, the total number of pets she has at the beginning is: \n7 (cats) + 12 (dogs) = 19 pets.",
"score": 0.97265625,
"scores": [
0.97265625
],
"is_final_answer": false
},
{
"path": "Olivia initially has 7 cats and 12 dogs. \nSo, the total number of pets she has at the beginning is: \n7 (cats) + 12 (dogs) = 19 pets.",
"score": 0.97265625,
"scores": [
0.97265625
],
"is_final_answer": false
},
{
"path": "Olivia currently has 7 cats and 12 dogs. \nSo, her total number of pets now is: \n7 (cats) + 12 (dogs) = 19 pets.",
"score": 0.96484375,
"scores": [
0.96484375
],
"is_final_answer": false
},
{
"path": "Olivia currently has 7 cats and 12 dogs. \nSo, her current total number of pets is: \n7 (cats) + 12 (dogs) = 19 pets.",
"score": 0.96484375,
"scores": [
0.96484375
],
"is_final_answer": false
}
]
},
{
"depth": 1,
"candidates": [
{
"path": "She adopts 2 more dogs, so the number of dogs becomes:\n$$ 12 + 2 = 14 $$",
"score": 1,
"scores": [
1,
1
],
"is_final_answer": false
},
{
"path": "She adopts 2 more dogs, so the number of dogs becomes:\n$$ 12 + 2 = 14 $$",
"score": 1,
"scores": [
1,
1
],
"is_final_answer": false
},
{
"path": "She adopts 2 more dogs, so the number of dogs becomes:\n$$ 12 + 2 = 14 $$",
"score": 1,
"scores": [
1,
1
],
"is_final_answer": false
},
{
"path": "She adopts 2 more dogs, so the number of dogs becomes:\n$$ 12 + 2 = 14 $$",
"score": 1,
"scores": [
1,
1
],
"is_final_answer": false
},
{
"path": "She adopts 2 more dogs and buys 2 more cats.",
"score": 1,
"scores": [
1,
1
],
"is_final_answer": false
},
{
"path": "She adopts 2 more dogs, so the number of dogs becomes:\n$$ 12 + 2 = 14 $$",
"score": 1,
"scores": [
1,
1
],
"is_final_answer": false
},
{
"path": "She adopts 2 more dogs, so the number of dogs becomes:\n$$ 12 + 2 = 14 $$",
"score": 1,
"scores": [
1,
1
],
"is_final_answer": false
},
{
"path": "She adopts 2 more dogs, so the number of dogs becomes:\n$$ 12 + 2 = 14 $$",
"score": 1,
"scores": [
1,
1
],
"is_final_answer": false
},
{
"path": "She adopts 2 more dogs, so the number of dogs becomes:\n$$ 12 + 2 = 14 $$",
"score": 1,
"scores": [
1,
1
],
"is_final_answer": false
},
{
"path": "She adopts 2 more dogs, so the number of dogs becomes:\n$$ 12 + 2 = 14 $$",
"score": 1,
"scores": [
1,
1
],
"is_final_answer": false
},
{
"path": "She adopts 2 more dogs, so the number of dogs becomes: \n12 + 2 = 14",
"score": 0.998046875,
"scores": [
1,
0.99609375
],
"is_final_answer": false
},
{
"path": "She adopts 2 more dogs, so the number of dogs becomes: \n12 + 2 = 14",
"score": 0.998046875,
"scores": [
1,
0.99609375
],
"is_final_answer": false
},
{
"path": "She adopts 2 more dogs, so the number of dogs becomes: \n12 + 2 = 14",
"score": 0.998046875,
"scores": [
1,
0.99609375
],
"is_final_answer": false
},
{
"path": "Adding 2 more dogs and 2 more cats:",
"score": 0.998046875,
"scores": [
1,
0.99609375
],
"is_final_answer": false
},
{
"path": "She adopts 2 more dogs, so the number of dogs becomes:\n12 + 2 = 14",
"score": 0.998046875,
"scores": [
1,
0.99609375
],
"is_final_answer": false
},
{
"path": "She adopts 2 more dogs, so the number of dogs becomes:\n12 + 2 = 14",
"score": 0.998046875,
"scores": [
1,
0.99609375
],
"is_final_answer": false
}
]
},
{
"depth": 2,
"candidates": [
{
"path": "She also buys 2 more cats, so the number of cats becomes:\n$$ 7 + 2 = 9 $$",
"score": 1,
"scores": [
1,
1,
1
],
"is_final_answer": false
},
{
"path": "She also buys 2 more cats, so the number of cats becomes:\n$$ 7 + 2 = 9 $$",
"score": 1,
"scores": [
1,
1,
1
],
"is_final_answer": false
},
{
"path": "She buys 2 more cats, so the number of cats becomes:\n$$ 7 + 2 = 9 $$",
"score": 1,
"scores": [
1,
1,
1
],
"is_final_answer": false
},
{
"path": "She buys 2 more cats, so the number of cats becomes:\n$$ 7 + 2 = 9 $$",
"score": 1,
"scores": [
1,
1,
1
],
"is_final_answer": false
},
{
"path": "She also buys 2 more cats, so the number of cats becomes:\n$$ 7 + 2 = 9 $$",
"score": 1,
"scores": [
1,
1,
1
],
"is_final_answer": false
},
{
"path": "She buys 2 more cats, so the number of cats becomes:\n$$ 7 + 2 = 9 $$",
"score": 1,
"scores": [
1,
1,
1
],
"is_final_answer": false
},
{
"path": "She buys 2 more cats, so the number of cats becomes:\n$$ 7 + 2 = 9 $$",
"score": 1,
"scores": [
1,
1,
1
],
"is_final_answer": false
},
{
"path": "She buys 2 more cats, so the number of cats becomes:\n$$ 7 + 2 = 9 $$",
"score": 1,
"scores": [
1,
1,
1
],
"is_final_answer": false
},
{
"path": "She also buys 2 more cats, so the number of cats becomes:\n$$ 7 + 2 = 9 $$",
"score": 1,
"scores": [
1,
1,
1
],
"is_final_answer": false
},
{
"path": "She buys 2 more cats, so the number of cats becomes:\n$$ 7 + 2 = 9 $$",
"score": 1,
"scores": [
1,
1,
1
],
"is_final_answer": false
},
{
"path": "She buys 2 more cats, so the number of cats becomes:\n$$ 7 + 2 = 9 $$",
"score": 1,
"scores": [
1,
1,
1
],
"is_final_answer": false
},
{
"path": "She also buys 2 more cats, so the number of cats becomes:\n$$ 7 + 2 = 9 $$",
"score": 1,
"scores": [
1,
1,
1
],
"is_final_answer": false
},
{
"path": "She buys 2 more cats, so the number of cats becomes:\n$$ 7 + 2 = 9 $$",
"score": 1,
"scores": [
1,
1,
1
],
"is_final_answer": false
},
{
"path": "She buys 2 more cats, so the number of cats becomes:\n$$ 7 + 2 = 9 $$",
"score": 1,
"scores": [
1,
1,
1
],
"is_final_answer": false
},
{
"path": "She buys 2 more cats, so the number of cats becomes:\n$$ 7 + 2 = 9 $$",
"score": 1,
"scores": [
1,
1,
1
],
"is_final_answer": false
},
{
"path": "She buys 2 more cats, so the number of cats becomes:\n$$ 7 + 2 = 9 $$",
"score": 1,
"scores": [
1,
1,
1
],
"is_final_answer": false
}
]
},
{
"depth": 3,
"candidates": [
{
"path": "Now, to find the total number of pets, we add the number of cats and dogs:\n$$ 14 + 9 = 23 $$",
"score": 1,
"scores": [
1,
1,
1,
1
],
"is_final_answer": false
},
{
"path": "Now, to find the total number of pets, we add the number of cats and dogs:\n$$ 14 + 9 = 23 $$",
"score": 1,
"scores": [
1,
1,
1,
1
],
"is_final_answer": false
},
{
"path": "Now, we add the total number of pets:\n$$ 14 + 9 = 23 $$",
"score": 1,
"scores": [
1,
1,
1,
1
],
"is_final_answer": false
},
{
"path": "Now, we add the total number of pets:\n$$ 14 + 9 = 23 $$",
"score": 1,
"scores": [
1,
1,
1,
1
],
"is_final_answer": false
},
{
"path": "Now, we add the total number of pets:\n$$ 14 + 9 = 23 $$",
"score": 1,
"scores": [
1,
1,
1,
1
],
"is_final_answer": false
},
{
"path": "Now, we add the total number of pets:\n$$ 14 + 9 = 23 $$",
"score": 1,
"scores": [
1,
1,
1,
1
],
"is_final_answer": false
},
{
"path": "Now, to find the total number of pets, we add the number of cats and dogs:\n$$ 14 + 9 = 23 $$",
"score": 1,
"scores": [
1,
1,
1,
1
],
"is_final_answer": false
},
{
"path": "Now, to find the total number of pets, we add the number of cats and dogs:\n$$ 14 + 9 = 23 $$",
"score": 1,
"scores": [
1,
1,
1,
1
],
"is_final_answer": false
},
{
"path": "Now, we add the total number of pets:\n$$ 14 + 9 = 23 $$",
"score": 1,
"scores": [
1,
1,
1,
1
],
"is_final_answer": false
},
{
"path": "Now, to find the total number of pets, we add the number of cats and dogs:\n$$ 14 + 9 = 23 $$",
"score": 1,
"scores": [
1,
1,
1,
1
],
"is_final_answer": false
},
{
"path": "Now, we add the total number of pets:\n$$ 14 + 9 = 23 $$",
"score": 1,
"scores": [
1,
1,
1,
1
],
"is_final_answer": false
},
{
"path": "Now, we add the total number of pets:\n$$ 14 + 9 = 23 $$",
"score": 1,
"scores": [
1,
1,
1,
1
],
"is_final_answer": false
},
{
"path": "Now, we add the total number of pets:\n$$ 14 + 9 = 23 $$",
"score": 1,
"scores": [
1,
1,
1,
1
],
"is_final_answer": false
},
{
"path": "Now, we add the total number of pets:\n$$ 14 + 9 = 23 $$",
"score": 1,
"scores": [
1,
1,
1,
1
],
"is_final_answer": false
},
{
"path": "Now, we add the total number of pets:\n$$ 14 + 9 = 23 $$",
"score": 1,
"scores": [
1,
1,
1,
1
],
"is_final_answer": false
},
{
"path": "Now, we add the total number of pets:\n$$ 14 + 9 = 23 $$",
"score": 1,
"scores": [
1,
1,
1,
1
],
"is_final_answer": false
}
]
},
{
"depth": 4,
"candidates": [
{
"path": "$$\n\\boxed{23}\n$$",
"score": 1,
"scores": [
1,
1,
1,
1,
1
],
"is_final_answer": true
},
{
"path": "$$\n\\boxed{23}\n$$",
"score": 1,
"scores": [
1,
1,
1,
1,
1
],
"is_final_answer": true
},
{
"path": "$$\n\\boxed{23}\n$$",
"score": 1,
"scores": [
1,
1,
1,
1,
1
],
"is_final_answer": true
},
{
"path": "$$\n\\boxed{23}\n$$",
"score": 1,
"scores": [
1,
1,
1,
1,
1
],
"is_final_answer": true
},
{
"path": "$$\n\\boxed{23}\n$$",
"score": 1,
"scores": [
1,
1,
1,
1,
1
],
"is_final_answer": true
},
{
"path": "$$\n\\boxed{23}\n$$",
"score": 1,
"scores": [
1,
1,
1,
1,
1
],
"is_final_answer": true
},
{
"path": "$$\n\\boxed{23}\n$$",
"score": 1,
"scores": [
1,
1,
1,
1,
1
],
"is_final_answer": true
},
{
"path": "$$\n\\boxed{23}\n$$",
"score": 1,
"scores": [
1,
1,
1,
1,
1
],
"is_final_answer": true
},
{
"path": "$$\n\\boxed{23}\n$$",
"score": 1,
"scores": [
1,
1,
1,
1,
1
],
"is_final_answer": true
},
{
"path": "$$\n\\boxed{23}\n$$",
"score": 1,
"scores": [
1,
1,
1,
1,
1
],
"is_final_answer": true
},
{
"path": "$$\n\\boxed{23}\n$$",
"score": 1,
"scores": [
1,
1,
1,
1,
1
],
"is_final_answer": true
},
{
"path": "$$\n\\boxed{23}\n$$",
"score": 1,
"scores": [
1,
1,
1,
1,
1
],
"is_final_answer": true
},
{
"path": "$$\n\\boxed{23}\n$$",
"score": 1,
"scores": [
1,
1,
1,
1,
1
],
"is_final_answer": true
},
{
"path": "$$\n\\boxed{23}\n$$",
"score": 1,
"scores": [
1,
1,
1,
1,
1
],
"is_final_answer": true
},
{
"path": "$$\n\\boxed{23}\n$$",
"score": 1,
"scores": [
1,
1,
1,
1,
1
],
"is_final_answer": true
},
{
"path": "$$\n\\boxed{23}\n$$",
"score": 1,
"scores": [
1,
1,
1,
1,
1
],
"is_final_answer": true
}
]
}
] |
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