Question

Joe's Painting charges $100 plus $20 per hour to paint the exterior of your home. Steve's Painting charges $120 plus $15 per hour to paint the exterior of your home. How many hours do Joe and Steve have to work for their models to be equal to each other? Which of the following systems is correct for this situation if "x" = hours worked and "y" = total income.

Answer 1

Joe's Painting: 20x + 100 = y

Steve's Painting: 15x + 120 = y

x = hours worked

y = total income

We can find when the two equations intersect by making them equal to each other. That means we put an equal sign in the middle. So, it would look something like this:

20x + 100 = 15x + 120

First, we have to move the 100 by subtracting it from both sides.

20x = 15x + 120 - (100)

20x = 15x + 20

Then, we need to move the 15x by subtracting it from both sides.

20 - (15x) = 20

5x = 20

Lastly, we need to divide 5 from both sides.

5x = 20/5

x = 4

Therefore, Joe and Steve would have to work for 4 hours in order for their models to be equal to each other.