2015 AMC 10A Problems/Problem 6
- The following problem is from both the 2015 AMC 12A #4 and 2015 AMC 10A #6, so both problems redirect to this page.
Contents
Problem
The sum of two positive numbers is times their difference. What is the ratio of the larger number to the smaller number?
Solution 1
Let be the bigger number and be the smaller.
.
Multiplying out gives and rearranging gives and factorised into and then solving gives
, so the answer is .
Solution 2
Without loss of generality, let the two numbers be and , as they clearly satisfy the condition of the problem. The ratio of the larger to the smaller is .
Video Solution (CREATIVE THINKING)
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Video Solution
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See Also
2015 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 5 |
Followed by Problem 7 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AMC 10 Problems and Solutions |
2015 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 3 |
Followed by Problem 5 |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
All AMC 12 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.