Question

Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.A business owner wants to have the front window of her store painted and is considering two artists for the job. Lena has quoted a flat rate of $191 for the job. Cara's quote is $20 per hour, plus $31 to cover the cost of materials. Depending on how long it takes Cara to paint the window, these two could end up charging the same amount. How long would Cara have to take? How much would it cost?

Answer 1

Given:

A business owner wants to have the front window of her store painted and is considering two artists for the job.

First, Lena has quoted a flat rate of $191 for the job.

so, y = 191

Second, Cara's quote is $20 per hour, plus $31 to cover the cost of materials.

So, y = 20x + 31

where x is the number of hours

so, we have the following system of equations:

`\begin{gathered} y=191\rightarrow(1) \\ y=20x+31\rightarrow(2) \end{gathered}`

solve using substitution,

so substitute with (y) from equation (1) into equation (2)

`191=20x+31`

Solve the equation to find (x)

`\begin{gathered} 20x=191-31 \\ 20x=160 \\ x=(160)/(20)=8 \end{gathered}`

so, the answer will be:

The number of hours = 8 hours

and the cost will be $191