Sample Question 6:

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?

$\textbf {(A) } 33 \qquad \textbf {(B) } 34 \qquad \textbf {(C) } 36 \qquad \textbf {(D) } 38 \qquad \textbf {(E) } 39$

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Answer Keys

Question 6: C

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Solutions

Question 6
Step 1: Note that Orvin gets a second balloon for $\frac{1}{3}$ off the regular price. So, the cost for each set of two balloons is $\frac{5}{3}$ of the regular price.

Step 2: Since Orvin had enough money to buy 30 balloons at the regular price, with the special sale, he now has enough to buy these sets of two balloons.

Step 3: So the number of sets of these two balloons Orvin can buy is $30 \times \frac{2}{\frac{5}{3}}$, which simplifies to $30 \times \frac{6}{5}$.

Step 4: Therefore, the maximum number of balloons Orvin can buy is $30 \times \frac{6}{5} = 36$, which matches with option (C).