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2018 AMC 12B Problem 6

Problem 6 of 25EasierAlgebra

Suppose SS cans of soda can be purchased from a vending machine for QQ quarters. Which of the following expressions describes the number of cans of soda that can be purchased for DD dollars, where 11 dollar is worth 44 quarters?

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Solution

One can costs QS\tfrac{Q}{S} quarters, which is Q4S\tfrac{Q}{4S} dollars. The number of cans that DD dollars can buy is DQ4S=4DSQ. \dfrac{D}{\tfrac{Q}{4S}}=\dfrac{4DS}{Q}. Thus, the correct answer is B.

More practice

Concepts: ratio and proportion · unit conversion

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