Question

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 $\frac{1}{3}$ off the regular price. What is the greatest number of balloons Orvin could buy?

$33$

$34$

$36$

$38$

$39$

Solution:

Suppose we buy $6$ balloons. Then, we can buy $3$ at full price and $3$ at a price of $\frac 23$ of a balloon.

Therefore, we can buy it at a price of $5$ balloons. Thus, with the money to buy $30$ balloons, we could buy $30 \cdot \frac 65 = 36$ balloons.

Thus, the correct answer is C .

2014 AMC 10B Problem 6

Solution:

Problem 6 in Other Years