Question

Select the correct answer.

Sam is an artist, and he wants to purchase frames to display his work at home. He wants to frame no fewer than 10 of his pieces, and he can spend a maximum of $225. Large frames cost $24, and medium frames cost $18.

Which system of inequalities can Sam use to determine the number of large frames, x, and medium frames, y, that he can purchase to meet his needs?

A.
18x + 24y ≤ 225
x + y ≥ 10
B.
24x + 18y ≥ 225
x + y ≤ 10
C.
18x + 24y ≥ 225
x + y ≤ 10
D.
24x + 18y ≤ 225

Answer 1

The correct answer is:

A.
24x + 18y ≤ 225
x + y ≥ 10

Explanation:
- \(24x + 18y \leq 225\) represents the constraint on the maximum amount of money Sam can spend on the frames. Since large frames cost $24 each and medium frames cost $18 each, this inequality ensures that the total cost does not exceed $225.
- \(x + y \geq 10\) represents the constraint that Sam wants to frame no fewer than 10 of his pieces, so the sum of the number of large frames (x) and medium frames (y) should be at least 10.