How do i solve a mixture problem usi g a system of linear equation

Question

Two mechanics worked on a car. The first mechanic worked for 5 hrs, and the second mechanic worked for 15hrs. 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 $195 per hr.

Answer 1

F + S = 195

5F + 15S = 1875

divide by 5

F + 3S = 375

subtract

F+S = 195

to get

2S = 180

S = 180/2 = $90 per hour for the Second mechanic

F = 195-90 = $105 per hour for the First mechanic

5(105) +15(90) = 525 + 1350 = 1875

105 + 90 = 195