Question

Luis can spend up to $240 buying men’s and women’s shirts for his club. Men’s shirts cost $8 each and women’s shirts cost $12 each. He needs to buy at least 3 of each type of shirt. Also, the women’s shirts must be at least twice the number of men’s shirts.

Which combinations of men’s and women’s shirts can Luis buy?

Choose all answers that are correct.

A. 4 men’s shirts and 9 women’s shirts

B. 5 men’s shirts and 8 women’s shirts

C. 6 men’s shirts and 15 women’s shirts

D. 7 men’s shirts and 17 women’s shirts

Answer 1

To find all the combinations you need to solve this system of inequations:

8m + 12w ≤ 240

m ≥ 3

w ≥ 3

w ≥ 2m

The way to solve that system is by graphing each inequation in the same system of coordinates (m,w).

From the combinations listed, 6 men's shirts and 15 women's shirts is the only valid one.

8*6 + 12*15 = 228 ≤ 240

6 ≥ 3

15 ≥ 3

15 ≥ 2(6)

Then, the answer is option C. 6 men's shirts and 15 women's shirts