Using a system of linear equations

Question

Two mechanics worked on a car. The first mechanic worked for
15
hours, and the second mechanic worked for
5
hours. Together they charged a total of
$1875
. What was the rate charged per hour by each mechanic if the sum of the two rates was
$165
per hour?

Answer 1

x = rate of mechanic who worked 15 hours.  That mechanic charged 15x.

y = rate of mechanic who worked 5 hours.  That mechanic charged 5y.

 

15x + 5y = 1875

x + y = 165

 

Solve for x and y.  

 

Top equation minus 5 times bottom equation gives

 

10x = 1875 - 5(165) = 1050

x = 1050/10 = 105

 

 

Plug x = 105 into bottom equation and get

 

y = 165 - 105 = 60

 

The 15 hour mechanic charged $105 per hour, and the 5 hour mechanic charged $60 per hour.