2016 AMC 10A Problem 3

Below is the professionally curated solution for Problem 3 of the 2016 AMC 10A, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2016 AMC 10A solutions, or check the answer key.

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Concepts:ratio and proportion money

Difficulty rating: 870

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?

$\$37.50$

$\$50.00$

$\$87.50$

$\$90.00$

$\$92.50$

Solution:

For each dollar Ben spent, David spent $75$ cents, so the difference was $25$ cents. The total difference $\$12.50$ is therefore one quarter of Ben's spending.

Ben spent $12.50\div0.25=50$ dollars, and David spent $37.50$ dollars. Together they spent $87.50$ dollars.

Thus, the correct answer is C.

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