Question

an auto shop has two mechanics. they charge a combined rate of $130 per hour. on their most recent car, the first mechanic worked for 15 hours, and the second mechanic worked for 5 hours. together they charged a total of $1500. what is the rate charged per hour by each mechanic? first mechanic: $□ per hour second mechanic: $□ per hour note that the aleks graphing calculator can be used to make computations easier.

Explanation:

Step1: Set up equations

Let the rate of the first mechanic be $x$ per hour and the rate of the second mechanic be $y$ per hour.
We know that $x + y=130$ (combined rate) and $15x + 5y = 1500$ (total charge equation).
From $x + y=130$, we get $y = 130 - x$.

Step2: Substitute and solve

Substitute $y = 130 - x$ into $15x + 5y = 1500$.

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Step3: Find the other rate

Substitute $x = 85$ into $y = 130 - x$.
$y=130 - 85=45$

Answer:

First mechanic: $85$ per hour, Second mechanic: $45$ per hour