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

https://youtu.be/VIt6LnkV4_w?t=81

https://youtu.be/tYU8ZZKar4A

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2016 AMC 10A (Problems • Answer Key • Resources)
Preceded by Problem 2	Followed by Problem 4
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All AMC 10 Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.

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