Question

Kyra is framing a square painting with side lengths of (x + 6) inches.

The total area of the painting and the frame has a side length of (2x −

5)

inches.

The material for the frame will cost $0.07

per square inch.

Answer 1

Complete Question:

Kyra is framing a square painting with side lengths of (x + 6) inches. The total area of the painting and the frame has a side length of (2x - 5) inches. The material for the frame will cost $0.07 per square inch.

Find the cost of the material for the frame is x = 16.

Answer:

The material cost of the frame is: $17.15

Step-by-step explanation:

Given

$L_1 = (x + 6)\ in$ --- Length of painting

$L_2 = (2x - 6)$ --- Frame and Painting

$Cost = \ 0.07$ per square inch

Required

The cost of material of the frame

First, we calculate the area of the frame only

This is the difference between the areas of the frame and painting and the area of the painting

$Area = (L_2)^2 - (L_1)^2$

$Area = (2x - 5)^2 - (x + 6)^2$

Substitute 16 for x

$Area = (2*16 - 5)^2 - (16 + 6)^2$

$Area = (27)^2 - (22)^2$

$Area = 245\ in^2$

The cost of the painting is:

$Total\ Cost = Unit\ Cost * Area$

$Total\ Cost = \ 0.07 * 245$

$Total\ Cost = \ 17.15$

Hence, the material cost of the frame is: $17.15