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Carlos began with twice as much money as David had. After Carlos gave $12 to David, Carlos still had $10 more than David. How much money did they have combined at the start?
- a)$34
- b)$68
- c)$102
- d)$108
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
Carlos began with twice as much money as David had. After Carlos gave ...
Let x = the number of dollars David had to start.
If Carlos started with twice as much money as David, then Carlos started with 2x dollars. After Carlos gave David $12, Carlos had 2x - 12 dollars and David had x + 12 dollars. If Carlos still had $10 more than David, then
2x - 12 = 10 + x + 12
Simplify: 2x - 12 = x + 22
Add 12: 2x = x + 34
Subtract x: x = 34
Therefore, David started with $34 and Carlos started with 2($34) = $68, so they had $34 + $68 = $102 combined to start.
If Carlos started with twice as much money as David, then Carlos started with 2x dollars. After Carlos gave David $12, Carlos had 2x - 12 dollars and David had x + 12 dollars. If Carlos still had $10 more than David, then
2x - 12 = 10 + x + 12
Simplify: 2x - 12 = x + 22
Add 12: 2x = x + 34
Subtract x: x = 34
Therefore, David started with $34 and Carlos started with 2($34) = $68, so they had $34 + $68 = $102 combined to start.
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Community Answer
Carlos began with twice as much money as David had. After Carlos gave ...
Analysis:
Let's first represent the amount of money Carlos and David had at the start.
Let x be the amount of money David had.
Carlos had twice as much money as David, so Carlos had 2x at the start.
After Carlos gave $12 to David, Carlos had 2x - 12 and David had x + 12.
Given information:
- After giving $12 to David, Carlos still had $10 more than David. This can be represented as:
2x - 12 = (x + 12) + 10
Solving the equation:
2x - 12 = x + 22
2x - x = 22 + 12
x = 34
Calculating the total amount at the start:
David had $34 at the start
Carlos had 2x = 2(34) = $68 at the start
Combined amount at the start = 34 + 68 = $102
Therefore, the correct answer is option C ($102).
Let's first represent the amount of money Carlos and David had at the start.
Let x be the amount of money David had.
Carlos had twice as much money as David, so Carlos had 2x at the start.
After Carlos gave $12 to David, Carlos had 2x - 12 and David had x + 12.
Given information:
- After giving $12 to David, Carlos still had $10 more than David. This can be represented as:
2x - 12 = (x + 12) + 10
Solving the equation:
2x - 12 = x + 22
2x - x = 22 + 12
x = 34
Calculating the total amount at the start:
David had $34 at the start
Carlos had 2x = 2(34) = $68 at the start
Combined amount at the start = 34 + 68 = $102
Therefore, the correct answer is option C ($102).
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