Question

ryan has a 20% off coupon to buy new clothes. he bought a shirt for $35 and socks for $7 per pair. he has to spend more than $75 to apply the coupon. how many socks can he buy?

Explanation:

Step1: Define variables and inequality

Let \( x \) be the number of socks. The cost of the shirt is \(\$35\) and each sock pair is \(\$7\), so total cost is \( 35 + 7x \). He needs to spend more than \(\$75\), so the inequality is \( 35 + 7x > 75 \).

Step2: Solve the inequality

Subtract 35 from both sides: \( 7x > 75 - 35 \)
Simplify: \( 7x > 40 \)
Divide both sides by 7: \( x > \frac{40}{7} \approx 5.71 \)

Since \( x \) must be an integer (number of socks), \( x \geq 6 \).

Answer:

Ryan can buy at least 6 pairs of socks.