2014 AMC 12B Problem 2

Problem 2 of 25EasierAlgebra

Orvin went to the store with just enough money to buy

30

balloons. When he arrived he discovered that the store had a special sale on balloons: buy

1

balloon at the regular price and get a second at

\tfrac13

off the regular price. What is the greatest number of balloons Orvin could buy?

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Solution

Under the sale, a pair of balloons costs

1 + \tfrac23 = \tfrac53

times the regular price of one balloon. Orvin’s money buys

30

balloons at the regular price, so he can afford

30 \div \tfrac53 = 18

pairs, which is

36

balloons. Thus, the correct answer is C.