Question

Two mechanics worked on a car. The first mechanic worked for 20 hours, and the second mechanic worked for 15 hours. Together they charged a total of $3875. What was the rate charged per hour by each mechanic if the sum of the two rates was $220 per hour?

Answer 1

To solve this problem we have to state a system of equations and solve it.

Let x and y be the rates charged per hour by each mechanic.

The sum of x and y is 220:

$x+y=220$

The sum of 20x and 15y is 3875:

$20x+15y=3875$

Solve the system by substitution:

$\begin{gathered} x=220-y \\ 20(220-y)+15y=3875 \\ 4400-20y+15y=3875 \\ -20y+15y=3875-4400 \\ -5y=-525 \\ y=\frac{-525}{-5} \\ y=105 \end{gathered}$

Use the value of y to find x:

$\begin{gathered} x=220-y \\ x=220-105 \\ x=115 \end{gathered}$

It means that the rates charged per hour by each mechanic were $115 and $105.