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 $725. What was the rate charged per hour by each mechanic if the sun of the two rates was $100 per hour?

You have two unknown rates, so we need to develop two equations to solve for these unknowns (based on the information given on the problem statement):

5x + 10y = 725

x + y = 100

By substitution, we get:

5x + 10 (100 - x) = 725

5x + 1000 - 10x = 725

-5x = 725 - 1000

-5x = - 275

x = - 275/-5 = 55

100 - 55 = 45

Thus:

The mechanic who worked for 5 hours charged his time at $55/hr, and the mechanic who worked for 10 hours charged his time at $45/hr.

To verify, plug and chug the results back into the original equations:

5 (55) + 10 (45) = 725

275 + 450 = 725

725 = 725 [OK]

55 + 45 = 100 [OK]