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2016 AMC 10A Problem 3

Problem 3 of 25EasierAlgebra

For every dollar Ben spent on bagels, David spent 2525 cents less. Ben paid $12.50\$12.50 more than David. How much did they spend in the bagel store together?

Answer choices

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Solution

For each dollar Ben spent, David spent 7575 cents, so the difference was 2525 cents. The total difference $12.50\$12.50 is therefore one quarter of Ben’s spending. Ben spent 12.50÷0.25=5012.50\div0.25=50 dollars, and David spent 37.5037.50 dollars. Together they spent 87.5087.50 dollars. Thus, the correct answer is C.

More practice

Concepts: ratio and proportion · money

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.