Question

the volume of olivia’s rectangular lunchbox is 240 cubic inches. the lunchbox is 3 inches deep, and its length is 2 inches more than its width. what is the width of olivia’s lunchbox?

Answer 1

8 inches

Explanation:

Volumn = Height*Width*Length

Width*(Width+2)=Volumn/Height=240/3=80

Width^2 +2Width-80=0

(Width-8)(Width+10)=0

Width>0 -> Width+10>0

-> Width-8=0 -> Width = 8 inches

Answer 2

The volume of the rectangular prism is:
v = (w) * (l) * (h)
Where,
w: width
l: length
h: height
Substituting values we have:
240 = (w) * (w + 2) * (3)
Rewriting we have:
80 = (w) * (w + 2)
80 = w ^ 2 + 2w
w ^ 2 + 2w - 80 = 0
The roots of the polynomial are:
w1 = -10
w2 = 8
We use the positive root because we are talking about dimensions.
w = 8 inches
Answer:
The width of olivia's lunchbox is:
w = 8 inches