Question

two mechanics worked on a car. the first mechanic worked for 20 hours, and the second mechanic for 15 hours. together they charged a total of $2950. what was the rate charged per hour by each mechanic if the sum of the two rates was $165 per hour?

Answer 1

Let 'x' be the rate per hour of the first mechanic and 'y' the rate per hour of the second mechanic.

It is said that the sum of those rates is $165 and that in 20 hours the first mechanic, and 15 hours the second mechanic, together they got $2950.

We can write a system of equations with this information:

`\begin{gathered} 20x+15y=2950 \\ x+y=165 \end{gathered}`

We can use the substitution method to solve this system. Let's clear y in the second equation

`y=165-x`

And replace this into the first equation

`20x+15(165-x)=2950`

And solve for x:

`\begin{gathered} 20x+15\cdot165-15x=2950 \\ 5x+2475=2950 \\ 5x=2950-2475 \\ 5x=475 \\ x=(475)/(5)=95 \end{gathered}`

With x = 95 se replace into the second equation we cleared before and find y:

`y=165-x=165-95=70`

The rate charged per hour by the first mechanic was $95 and by the second mechanic was $70