Question

A 7 by 10 inch mirror was put in a frame and hung on the wall. The mirror and frame together cover an area of 130 inches squared. How wide is the frame?

Answer 1

Answer: the width of the frame is 3 inches.

Step-by-step explanation:

Let x represent the width of the frame.

If the length of the mirror is 10 inches, the length of the mirror and the frame would be (x + 10) inches

If the width of the mirror is 7 inches, the width of the mirror and the frame would be (x + 7) inches

The mirror and frame together cover an area of 130 inches squared. This means that

(x + 10)(x + 7) = 130

x² + 7x + 10x + 70 = 130

x² + 17x + 70 - 130 = 0

x² + 17x - 60 = 0

x² + 20x - 3x - 60 = 0

x(x + 20) - 3(x + 20) = 0

x - 3 = 0 or x + 20 = 0

x = 3 or x = - 20

Since the width cannot be negative, then x = 3