2018 AMC 12B Problem 6

Attempt Problem 6 of the 2018 AMC 12B below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2018 AMC 12B solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

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?

\dfrac{4DQ}{S}

\dfrac{4DS}{Q}

\dfrac{4Q}{DS}

\dfrac{DQ}{4S}

\dfrac{DS}{4Q}

One can costs

\tfrac{Q}{S}

quarters

Convert

D

dollars to

4D

quarters, then divide by the price per can

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.

Problem 6 in other years