Question

Cary calculated the surface area of a box in the shape of a rectangular prism. She wrote the equation

148-2(6w+5h+w) 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?
a. W= 148-6h/ 12+h
b. w=148-12h/ 12+2h
c. w=136-14h
d. w-136-10h

Answer 1

The equivalent equation to Cary's solution of w = 74 - 6h/(h + 6) for the width of the box is Option A: w = (148 - 6h) / (12 + h).

Step-by-step explanation:

Cary calculated the surface area of a rectangular prism using the equation 148-2(6w+5h+w). When solving for w, she got w = 74 - 6h/(h + 6). To determine which of the provided options is equivalent to Cary's equation, we need to compare the outcomes of each option with Cary's solution when substituting in different values for h.

Option A: w = (148 - 6h) / (12 + h) - This simplifies to w = 74 - 6h/(h + 6), which is the same as Cary's solution.

Option B: w = (148 - 12h) / (12 + 2h) - This does not simplify to the same form as Cary's solution.

Option C: w = 136 - 14h - This is a linear equation without a denominator, thus not equivalent to Cary's equation.

Option D: w = 136 - 10h - Similarly, this is also a linear equation without a denominator, hence not equivalent to Cary's equation.

The only equivalent equation to Cary's solution is Option A: w = (148 - 6h) / (12 + h).