Solving a value mixture problem using a system of linear

Question

Two mechanics worked on a car. The first mechanic worked for 10 hours and the second mechanic worked for 5 hours. Together they charged a total of $775. What was the rate charged per hour by each mechanic if the sum of the two rates was $110 per hour

Answer 1

10x + 5y = 775

x + y = 110 means that y = 110 – x

Substitution: replace y with 110 – x in the 1st equation.

10x + 5(110 – x) = 775

10x + 550 – 5x = 775

10 – 5x = 775 – 550 = 225

5x = 225

x = 225/5 = 45

y = 110 – 45 = 65

One mechanic charged $45/hr

The other charged $65/hr

Check

10(45) + 5(65) = 450 + 325 = 725