Solving a value mixture problem using a system of linear equations

Question

Two mechanics worked on a car. The first mechanic charged $115 per hour, and the second mechanic charged $65 per hour. The mechanics worked for a combined total of 15 hours, and together they charged a total of $1475. How long did each mechanic work?

Answer 1

Start by declaring the variables using the units defined by the question. In this case, the question asks for time, so x is going to represent the number of hours the $65/hour mechanic worked and y will represent the number of hours the $115/hr mechanic worked. The two equations would then be:

x + y = 15

65x + 115y = 1475

substituting (15-y) for x in the second equations yields y = 10

and then x = 5!

The more expensive mechanic worked 10 hours and his cheaper coworker worked 5 hours.