Question

A cube has side length x. One side of the cube is increased by 4 inches, and another side is doubled. The volume of the new rectangular prism is 450 cubic inches. The equation 2x3+8x=450 can be used to find x. What was the side length of the original cube? Use a graphing calculator and a system of equations to find the answer.4 inches 5 inches 9 inches 10 inches

Answer 1

Check the picture below.

from that system of equations, we get x ≈ 5.84.

recall that for a system of equations, the solution is where the graph meet.

Answer 2

Let

x-------> the length side  of the original cube

we have

$2x^{3} +8x=450\\2x^{3}=450-8x$

Divide by $2$ both sides

$x^{3}=225-4x$

The system of equations is equal to

$y=x^{3}$ --------> equation $1$

$y=225-4x$ --------> equation $2$

using a graphing tool

see the attached figure  

we know that

the solution of the system of equations is the intersection both graphs

therefore

the solution is

$x=5.86\ in$

therefore

the answer is

$5.86\ inches$