Answer: Option C, she used the wrong symbol in the first inequality.
Step-by-step 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
