Two mechanics worked on a car. The first mechanic charged $45 per hour, and the second mechanic charged $105 per hour. The mechanics worked for a combined total

Question

Two mechanics worked on a car. The first mechanic charged $45 per hour, and the second mechanic charged $105 per hour. The mechanics worked for a combined total of 35 hours, and together they charged a total of $2475. How long did each mechanic work?

Answer 1

Hi again, Delaney-

Here is another case where we have two unknowns (the number of hours each mechanic worked) so we'll need two equations to solve.

Let A = number of hours first mechanic worked (the one who charged $45/hour)

Let B = number of hours second mechanic worked (the one who charged $105/hour)

From the problem statement, we know that the two mechanics worked a combined 35 hours so the first equation is:

Equation 1: A hours + B hours = 35 hours

We also know that in total, the charge was $2475.  So the second equation is:

Equation 2: (A hours x 45 dollars/hour) + (B hours x 105 dollars/hour) = 2475 dollars

So our two equations are:

1: A + B = 35

2: 45A + 105B = 2475

Multiply both sides of the first equation by -45 to get the following:

-45A - 45B = -1575

Now the two equations are:

1: -45A - 45B = -1575

2: 45A + 105B = 2475

Add them together and the "A" term drops out:

-45B + 105B = -1575 + 2475

or

60B = 900

Now divide both sides by 60:

B = 15

Now plug B = 15 into the first equation:

A + 15 = 35 thus A = 20

So Mechanic A (at $45/hour) worked 20 hours and Mechanic B (at $105/hour) worked 15 hours

 

Check: 20x45 + 15x105 = 900 + 1575 = 2475 

 

Answer 2

Let x = # hours by "$45 per hour" mechanic and x = # hours by other ($105/hr) Expert Mechanic.

 

x + y = 35

45x + 105 y = 2475

 

A system of two equations in two unknowns...you can solve it!