# 2016 AMC 10A Problems/Problem 3

## Problem

For every dollar Ben spent on bagels, David spent $25$ cents less. Ben paid $12.50$ more than David. How much did they spend in the bagel store together? $\textbf{(A)}\ 37.50 \qquad\textbf{(B)}\ 50.00\qquad\textbf{(C)}\ 87.50\qquad\textbf{(D)}\ 90.00\qquad\textbf{(E)}\ 92.50$

## Solution 1

If Ben paid $12.50$ more than David, then he paid $\frac{12.5}{.25}= 50.00$. Thus, David paid $37.50$, and they spent $50.00+37.50 = 87.50 \implies \boxed{\textbf{(C) } 87.50}$.

## Solution 2

If for every dollar Ben spent on bagels David spent $25$ cents less, then the ratio of the money that Ben spent to David spent is $4:3$. We know that Ben paid $12.50$ more than David, so we can write $12.50\cdot (4+3)= 87.50.$ Then the answer is $\boxed{\text{(C)}}.$

~@azure123456

## Video Solution (HOW TO THINK CREATIVELY!!!)

https://youtu.be/huMBaF16tlM


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## Video Solution

~savannahsolver

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