2018 AMC 12B Problem #6

Algebra Level 3

Suppose S S cans of soda can be purchased from a vending machine for Q Q quarters. Which of the following expressions describes the number of cans of soda that can be purchased for D D dollars, where 1 dollar is worth 4 quarters?

This problem is part of the 2018 AMC 12B .
4 D Q S \dfrac{4DQ}{S} 4 D S Q \dfrac{4DS}{Q} D S 4 Q \dfrac{DS}{4Q} 4 Q D S \dfrac{4Q}{DS} D Q 4 S \dfrac{DQ}{4S}

Steven Yuan by Steven Yuan , 20, USA

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2 solutions

Chew-Seong Cheong
Feb 17, 2018

Q Q quarters = Q 4 =\dfrac Q4 dollars. Q 4 \dfrac Q4 dollars get S S cans of soda. Therefore the price of one can of soda is Q 4 S = Q 4 S \dfrac {\frac Q4}S = \dfrac Q{4S} . And D D dollars can buy D Q 4 S = 4 D S Q \dfrac D{\frac Q{4S}} = \boxed{\dfrac {4DS}Q} .

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Marta Reece
Feb 16, 2018

If you have D quarters, you can get D Q ⋅ S \frac{D}Q\cdot S sodas.

For D dollars, you get 4 times more, that is 4 D S Q \boxed{\frac{4DS}Q}

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