Question

an auto shop has two mechanics. they charge a combined rate of $165 per hour. on their most recent car, the first mechanic worked for 10 hours, and the second mechanic worked for 15 hours. together they charged a total of $2000. what is the rate charged per hour by each mechanic? first mechanic: $ per hour second mechanic: $ per hour

Explanation:

Step1: 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 $x + y=165$, so $y = 165 - x$.

Step2: Set up an equation based on the total charge.

The first mechanic worked 10 hours and the second worked 15 hours, and the total charge was $2000$. So, $10x+15y = 2000$.

Step3: Substitute $y = 165 - x$ into the second - equation.

$10x+15(165 - x)=2000$.
Expand the left - hand side: $10x + 2475-15x=2000$.
Combine like terms: $- 5x=2000 - 2475$.
$-5x=-475$.

Step4: Solve for $x$.

Divide both sides by $-5$: $x=\frac{-475}{-5}=95$.

Step5: Solve for $y$.

Since $y = 165 - x$, substitute $x = 95$ into this equation. So, $y=165 - 95 = 70$.

Answer:

First mechanic: $95$ per hour
Second mechanic: $70$ per hour