Question

an auto shop has two mechanics. they charge a combined rate of $170 per hour. on their most recent car, the first mechanic worked for 20 hours, and the second mechanic worked for 15 hours. together they charged a total of $2925. what is the rate charged per hour by each mechanic? note that the aleks graphing calculator can be used to make computations easier. first mechanic: $ per hour second mechanic: $ per hour

Explanation:

Step1: Let the rate of the first mechanic be $x$ per hour and the rate of the second mechanic be $y$ per hour.

We have two - equations based on the given information.
Equation 1 (combined rate): $x + y=170$, so $y = 170 - x$.
Equation 2 (total charge): $20x+15y = 2925$.

Step2: Substitute $y = 170 - x$ into the second equation.

$20x+15(170 - x)=2925$.
Expand the left - hand side: $20x + 2550-15x=2925$.
Combine like terms: $5x+2550 = 2925$.

Step3: Solve for $x$.

Subtract 2550 from both sides: $5x=2925 - 2550$.
$5x = 375$.
Divide both sides by 5: $x=\frac{375}{5}=75$.

Step4: Solve for $y$.

Since $y = 170 - x$, substitute $x = 75$ into this equation.
$y=170 - 75 = 95$.

Answer:

First mechanic: $75$ per hour
Second mechanic: $95$ per hour