solving a value mixture problem using a system of linear equation

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 $3150

. What was the rate charged per hour by each mechanic if the sum of the two rates was $185

 per hour?

first mechanic per hour ?

second mechanic per hour?

Answer 1

20F + 15S = 3150

F+S = 185

multiply both sides by 15

15F +15S = 2775

subtract last equation from the 1st to get

5F = 3150-2775 = 375

F = 375/5 = $75 per hour for the First mechanic

S = $110 per hour for the Second mechanic

20(75) +15(110) = 1500 + 1650 = 3150