Solving a value mixture problem using a system of linear equations

Question

Two mechanics worked on a car. The first mechanic worked for 20 hrs, and the second mechanic worked for 15 hrs. Together they charged a total of $2525. What was the rate charged per hr by each mechanic if the sum of the two rates was $150 per hr?

Answer 1

20F +15S = 2525

F+S = 150

15F + 15S = 15(150) = 2250

20F-15F =2525-2250 = 275

5F = 275

F = 275/5 = $55 per hour for First Mechanic

S = 150-55 = $95 per hour for Second Mechanic

20(55) +15(95)

=1100 + 1425

= 2525