2018 AMC 12B Problem 6

Problem 6 of 25EasierArithmetic

Suppose

S

cans of soda can be purchased from a vending machine for

Q

quarters. Which of the following expressions describes the number of cans of soda that can be purchased for

D

dollars, where

1

dollar is worth

4

quarters?

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Solution

One can costs

\tfrac{Q}{S}

quarters, which is

\tfrac{Q}{4S}

dollars. The number of cans that

D

dollars can buy is

\dfrac{D}{\tfrac{Q}{4S}}=\dfrac{4DS}{Q}.

Thus, the correct answer is B.

Tagged: ratio and proportion · unit conversion