Question

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.

A business owner wants to have the front window of his store painted and is considering two artists for the job. John has quoted a flat rate of $88 for the job. Zachary's quote is $5 per hour, plus $78 to cover the cost of materials. Depending on how long it takes Zachary to paint the window, these two could end up charging the same amount. How long would Zachary have to take? How much would it cost?
If the job takes Zachary hours, the cost would be $ with either artist.

Answer 1

Let's use the variable x to represent the number of hours it takes Zachary to paint the window. Then, we can write the following system of equations:

John's quote: y = 88

Zachary's quote: y = 5x + 78

We want to find the value of x where John's quote and Zachary's quote are equal, so we can set the two expressions for y equal to each other and solve for x:

88 = 5x + 78

Subtract 78 from both sides:

10 = 5x

Divide by 5:

x = 2

So Zachary would have to take 2 hours to charge the same amount as John's flat rate of $88.

To find how much it would cost, we can substitute x = 2 into Zachary's quote:

y = 5x + 78
y = 5(2) + 78
y = 10 + 78
y = 88

So if the job takes Zachary 2 hours, the cost would be $88 with either artist.