Ms. Silver wants to hire a painter to paint her house. Painters Plus charges $2,220 plus $45 per hour of labor. Davis & Sons charges $1,850 plus $65 per hour of labor. Write and solve an equation to determine the number of hours for which to two costs would be the same.

We know that cost depends on the number of hours worked.

Let cost = y

Let hours = x

We use these variables and the information to create equations for both companies.

Painters Plus

y = 45x + 2220

Davis & Sons

y = 65x + 1850

Since we want there costs to be the same, we equation the two.

45x + 2220 = 65x + 1850

Now solve for x to find the number of hours needed to work to make the same money.

Subtract 45x on both sides of equation.

2220 = 20x + 1850

Subtract 1850 on both sides of equation.

370 = 20x

Divide both sides of equation by 20.

18.5 = x

Both companies need to work 18.50 hours to make the same money.

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