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Sample 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).
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?
\(\textbf {(A) } 33 \qquad \textbf {(B) } 34 \qquad \textbf {(C) } 36 \qquad \textbf {(D) } 38 \qquad \textbf {(E) } 39\)
Answer Keys
Question 6: CSolutions
Question 6Step 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).