Difference between revisions of "2015 AMC 10A Problems/Problem 6"
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==Solution 2== | ==Solution 2== | ||
| − | Without loss of generality, let the two numbers be <math>3</math> and <math>2</math>, as they clearly satisfy the condition of the problem. The ratio is <math>\boxed{\textbf{(B) }\frac32}</math>. | + | Without loss of generality, let the two numbers be <math>3</math> and <math>2</math>, as they clearly satisfy the condition of the problem. The ratio of the larger to the smaller is <math>\boxed{\textbf{(B) }\frac32}</math>. |
==Video Solution== | ==Video Solution== | ||
Revision as of 18:49, 24 April 2022
- The following problem is from both the 2015 AMC 12A #4 and 2015 AMC 10A #6, so both problems redirect to this page.
Problem
The sum of two positive numbers is 
times their difference. What is the ratio of the larger number to the smaller number?
Solution
Let 
be the bigger number and 
be the smaller.
.
Multiplying out gives 
and rearranging gives 
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
~savannahsolver
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. 
