2015 AMC 12A Problems/Problem 10: Difference between revisions
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Integers <math>x</math> and <math>y</math> with <math>x>y>0</math> satisfy <math>x+y+xy=80</math>. What is <math>x</math>? | Integers <math>x</math> and <math>y</math> with <math>x>y>0</math> satisfy <math>x+y+xy=80</math>. What is <math>x</math>? | ||
<math> \textbf{(A)}\ 8 \qquad\textbf{(B)}\ 10 \qquad\textbf{(C)}\ 15 \qquad\textbf{(D) | <math> \textbf{(A)}\ 8 \qquad\textbf{(B)}\ 10 \qquad\textbf{(C)}\ 15 \qquad\textbf{(D)}\ 18 \qquad\textbf{(E)}\ 26</math> | ||
==Solution== | ==Solution== | ||
Revision as of 12:22, 29 March 2015
Problem
Integers 
and 
with 
satisfy 
. What is ?
Solution
Use SFFT to get 
. The terms 
and 
must be factors of 
, which include 
. Because 
, 
is equal to 
or . But if 
, then 
and so 
.
See Also
| 2015 AMC 12A (Problems • Answer Key • Resources) | |
| Preceded by Problem 9 |
Followed by Problem 11 |
| 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 | |
