Question

an auto shop has two mechanics. they charge a combined rate of $110 per hour. on their most recent car, the first mechanic worked for 20 hours, and the second mechanic worked for 5 hours. together they charged a total of $1525. what is the rate charged per hour by each mechanic? first mechanic: $per hour second mechanic: $per hour

Explanation:

Step1: Set up equations

Let the rate of the first mechanic be \(x\) dollars per hour and the rate of the second mechanic be \(y\) dollars per hour.
We know that \(x + y=110\) (combined rate) and \(20x + 5y=1525\) (total charge).
From \(x + y=110\), we get \(y = 110 - x\).

Step2: Substitute and solve

Substitute \(y = 110 - x\) into \(20x + 5y=1525\):

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Step3: Find the other rate

Substitute \(x = 65\) into \(y=110 - x\), we get \(y=110 - 65 = 45\)

Answer:

First mechanic: \(\$65\) per hour, Second mechanic: \(\$45\) per hour