The volume of a cuboid is = length × width × height.
Let the width of Olivia's lunch box be 'x'.
Hence the length of Olivia's lunch box shall be 'x + 2'
Also the height of the box is given as 3 inches.
The volume of the box is 240 in³
Substituting in the formula we get
[tex] x(x+2)(3) =240 [/tex]
Dividing by 3 on both sides
[tex] x(x+2)=80 [/tex]
Exapnding we get
[tex] x^2+2x=80 [/tex]
Subtracting 80 from both sides
[tex] x^2+2x-80=0 [/tex]
Factoring
[tex] (x+10)(x-8)=0 [/tex]
We get
x= -10 or x = 8
But x cannot be negative
So x = 8
Hence the width of the box is 8 inches.
