Question

Stephen and Karen are getting the floor redone in their house. Company A charges $215 and $.50 per square foot to install carpet. Company B charges $100 and $0.75 per square foot to install carpet. determine which company would be a better choice if stephen and karen were having 1000 square feet of carpet installed. Justify your answer using a math. Write and solve an equation to determine the exact square footage of the house that would cause the price for the two companies to be the same. What is the square footage that would cause the cost to be the same ?

Answer 1

The net charge offered by Company A for 1000 square feet of carpet.

`215+(0.5*1000)=715`

The net charge offered by Company B for 1000 square feet of carpet.

`100+(0.75*1000)=850`

The charge of Company A is less. Hence it is better.

Let x be the number of squar feet.

For company A,

`215+0.5x\ldots\ldots(1)`

For company B,

`100+0.75x\ldots\ldots(2)`

Equate (1) and (2) implies,

`\begin{gathered} 215+0.5x=100+0.75x \\ 115=0.25x \\ x=460 \end{gathered}`

Therefore, the number of square feet is 460.