Question

The volume of a rectangular prism is a minimum of 25 cubic feet. The height of the prism is 3 feet more than its width, and its length is at most 5 feet more than the width.

Carla wrote this system of inequalities to represent this situation, where V is the volume of the prism and w is the width.

Answer 1

C

Explanation:

Answer 2

Answer: Option C, she used the wrong symbol in the first inequality.

Explanation:

For a rectangular prism of length L, width W and height H, the volume is:

V = L*W*H

We know that the volume of the prism is a minimum of 25 ft^3

Then:

V ≥ 25ft^3

We also know that:

"The height of the prism is 3 feet more than its width"

H = W + 3ft

"and its length is at most 5 feet more than the width"

L ≤ W + 5ft

Then we have the system:

V ≥ 25ft^3

H = W + 3ft

L ≤ W + 5ft

Now we can rewrite the volume as:

V = L*W*H

V = L*W*(W + 3ft)

Now we can replace L by the inequality L ≤ W + 5ft

Then we get:

V ≤ (W + 5ft)*W*(W + 3ft)

V ≤ W^3 + 8ft*W^2 + 15ft*W

Then the inequalities are:

V ≤ W^3 + 8ft*W^2 + 15ft*W

V ≥ 25ft^3

Then the error in Carla's system is the symbol of the first inequality, where Carla used "<" instead of "≤"

The correct option is C