2014-09-10 09:00:12

A store is having a sale in which all DVDs are reduced in price by 15%. Additionally, the store offers a promotion in which one DVD is sold for half off the cost when another DVD is purchased at the original sale price. If two DVDs together cost $30.60, what was the price of ONE DVD before the sale took effect?

(A) $15
(B) $18
(C)  $20
(D) $24
(E) $25

The correct answer is D
Explanation: $30.60 is the price of the two DVDs after a couple changes. Let the original price be x dollars. The first DVD was sold at a 15% reduction, meaning it sold at .85x (since 100% - 15% would be 85% of the price). The second DVD sold at half that price, meaning it sold at .425x. Thus, the price of the two DVDs is .85x + .425x, or 1.275x. 1.275x is equal to 30.60, so x can be determined by using the equation

1.275x = 30.60

Divide both sides by 1.275 to isolate x, leaving x = 24. Thus, the price of one DVD was originally $24, making choice D correct.