Solving a value mixture problem using a system of linear equations

Question

Two mechanics worked on a car. The first mechanic charged $105 per hour, and the second mechanic charged $110 per hour. The mechanics worked for a combined total of 35 hours, and together they charged a total of $3750 . How long did each mechanic work?

Answer 1

Let a = hours for first mechanic

b = hours for the second mechanic

Then

a + b = 35

and 105a + 110b = 3750

Solving the two equations simultaneously, we find that a = 20 & b = 15

First Mechanic worked 20 hours

Second Mechanic worked 15 hours