Question

Cary calculated the surface area of a box in the shape of a rectangular prism. She wrote the equation 148=2(6w+6h+hw) to represent the width and height of the box. She solved for w and got w=74-6h/h+6 Which of the following is an equivalent equation? 

1.w=148-6h/12+h
2.w=148-12h/12+2h
3.w=136-14h
4.w=136-10h

Answer 1

Just took the quiz.

The answer is w = 148-12h/12+2h

Answer 2

Answer: 2.
`(148-12h)/(12+2h)`

Explanation:

Given: Cary calculated the surface area of a box in the shape of a rectangular prism.

The equation written by Cary to represent the width and height of the box. :

`148=2(6w+6h+hw)`

If we open the bracket on the right side, we get

`148=12w+12h+2hw\\\\\Rightarrow148=12h+12w+2hw\\\\\Rightarrow148=12h+w(12+2h)\\\\\Rightarrow148-12h=w(12+2h)\\\\\Rightarroww=(148-12h)/(12+2h)`

Hence the equation is equivalent to the equation written by Cary after solved for w
`w=(74-6h)/(h+6)` is
`(148-12h)/(12+2h)`