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
x + y ≥ 10
The correct system of inequalities is:
18x + 24y ≤ 225
x + y ≥ 10
This is because Sam wants to frame no fewer than 10 of his pieces, so the total number of frames (x + y) must be greater than or equal to 10. Additionally, he can spend a maximum of $225, so the cost of the frames (18x + 24y) must be less than or equal to $225.
Therefore, Option A is the correct answer.