Question

Jessica bought a few pairs of socks for $ 50. If there had been a 20% discount, she could have bought 5 more pairs of socks for the same total price. How many pairs of socks did she buy?

• A. 5
• B. 2
• C. 10
• D. 15
• E. 20

Hint:

In discount problems, equating original and discounted purchase conditions is the key step.

Answer 1

The Correct Option is C

Step 1: Let number of pairs bought be \( n \). Price per pair = \( \frac{50}{n} \).

Step 2: With 20% discount, price per pair = \( 0.8 \times \frac{50}{n} = \frac{40}{n} \).

Step 3: For same $ 50, pairs = \( \frac{50}{40/n} = \frac{50n}{40} = \frac{5n}{4} \).

Step 4: This is 5 more pairs: \( \frac{5n}{4} = n+5 \).

Step 5: Solve: \( 5n = 4n + 20 \Rightarrow n = 20 \).
Final Answer: \[ \boxed{20} \]