Question

Two mechanics worked on a car. The first mechanic worked for 10 hours, and the second mechanic worked for 15 hours together they charged a total of $2175. What was the rate charged per hour by each mechanic if the sum of the two rates was $170 per hour?

Answer 1

Answer:

Step-by-step explanation:

We need a system of equations here, 2 equations for 2 unknowns. The unknowns will be x and y and will represent the rates of 2 mechanics. The first equation will relate the 2 mechanics' rates and the second will involve the total they charged at their respective rates having worked a specific number of hours on the car.

We are told that the 2 rates added together was 170 per hour, so the first equation will be

x + y = 170

The next equation will be the rates times the number of hours worked:

10x + 15y = 2175 This means that the mechanic charging x dollars per hour worked on the car for 10 hours, and the mechanic charging y dollare per hour worked on the car for 15 hours, and that the amount this added up to was 2175.

We solve the first equation for y, just because. You could also solve it for x, if you want. Doesn't matter; you'll get the same answer either way.

y = 170 - x and sub that for y in the the second equation. Then we will have an equation with only 1 unknown in it:

10x + 15(170 - x) = 2175 and

10x + 2550 - 15x = 2175 and

-5x = -375 so

x = 75. One mechanic, the one who worked for 10 hours on te car, charges 75 per hour. To find out how much the other guycharges, go back to the first equation and sub in 75 for x:

75 + y = 170 so

y = 95 per hour.