2015 AMC 12A Problems/Problem 10

Problem

Integers $x$ and $y$ with $x>y>0$ satisfy $x+y+xy=80$. What is $x$?

$\textbf{(A)}\ 8 \qquad\textbf{(B)}\ 10 \qquad\textbf{(C)}\ 15 \qquad\textbf{(D)}\ 18 \qquad\textbf{(E)}\ 26$

Solution

Use SFFT to get $(x+1)(y+1)=81$. The terms $(x+1)$ and $(y+1)$ must be factors of $81$, which include $1, 3, 9, 27, 81$. Because $x > y$, $x+1$ is equal to $27$ or $81$. But if $x+1=81$, then $y=0$ and so $x=\boxed{\textbf{(E)}\ 26}$.

Video Solution

https://youtu.be/ba6w1OhXqOQ?t=4512

~ pi_is_3.14

See Also

2015 AMC 12A (ProblemsAnswer KeyResources)
Preceded by
Problem 9
Followed by
Problem 11
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All AMC 12 Problems and Solutions
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