# Difference between revisions of "2015 AMC 10B Problems/Problem 3"

## Problem

Kaashish has written down one integer two times and another integer three times. The sum of the five numbers is $100$, and one of the numbers is $28$. What is the other number?

$\textbf{(A) }8\qquad\textbf{(B) }11\qquad\textbf{(C) }14\qquad\textbf{(D) }15\qquad\textbf{(E) }18$

## Solution

Let the first number be $x$ and the second be $y$. We have $2x+3y=100$. We are given one of the numbers is $28$. If $x$ were to be $28$, $y$ would not be an integer, thus $y=28$. $2x+3(28)=100$, which gives $x=\boxed{\textbf{(A) }8}$.

~savannahsolver