Question

Katy recently hired a contractor to do some necessary work. On the final bill, Katy was charged a total of $488. $260 was listed for parts and the rest for labor. If the hourly rate for labor was $57, how many hours of labor was needed to complete the job? (A) First write an equation you can use to answer this question. Use x as your variable.(B) Solve your equation in part (A) to find the number of labor hours needed to do the job.

Answer 1

(A) $260 + $57x = $488

(B) 4 hours

Explanation:

(A) We need to find out how many hours of labor he needed to complete the job. That's what the x will represent.

We know that he charged Katy for the parts and for the labor, with an hourly rate of $57.

We need to sum the amount of money he charged for the parts with the hourly rate multiplied by the number of hours he worked.

Let's notice that we multiply the number of hours just to the hourly rate, the price of the parts doesn't depend on how many hours he worked.

That is $260 + $57*x

We know that the total was $488, so we just need to equal the expression before to the total.

$260 + $57x = $488

That's the expression we were looking for.

(B) Let's solve the equation. We need to leave the x alone on one side of the equation.

First, let's subtract $260 on both sides:

$260 + $57x - $260 = $488 - $260

$57x = $228

Now we divide by $57 on both sides:

$57x/$57 = $228/$57

x = 4

He needed 4 hours to do the job.