Math Word Problem

Question

Two mechanics worked on a car, the first mechanic worked for 20 hours and the second mechanic worked for

15 hours and together they charged a total of $2625.

what was the rate charged per hour by each mechanic if the sum of the two rates was $160 per hour?

Answer 1

Let x = rate per hour of the first mechanic and y = rate per hour of the second mechanic

Then, x + y = 160 and 20x + 15y = 2625.

Since x + y = 160, y = 160 - x.

So. 20x + 15(160 - x) = 2625

5x = 225

x = 45 and y = 115

The first mechanic charged $45 per hour while the second charged $115 per hour.

Answer 2

MECH 1 I MECH 2

20X I 15(160 - X)

I

I

I

I like to set up a key to help us with what we know. We will mark Mechanic 1 as X since we know the least about him. We do know that he worked 20 hours, so we will set Mechanic 1 as 20X. We know that Mechanic 2 worked for 15 hours. We also know that the total hourly rate for both mechanics is $160. So, let's multiply 15 by 160 - X, because 160 - X would be Mechanic 2's hourly rate. Why? Because X refers to Mechanic 1's pay. So, if we subtract his pay, we will have Mechanic 2's pay.

Now, let's set it all up!

20X + 15 (160-X ) = 2625 (remember that 2625 is the total, which is the sum, which is =

20X +2400 - 15X = 2625 (we need to distribute 15 x 160 and 15 x X)

5X = 225 (combine like terms, and subtract 2400 from each side)

X = 45 (now we know that Mechanic 1 (aka X) made $45 per hour

How much does Mechanic 2 make? Well, if we look back at the key we made, Mechanic 2 made 160 - X, and 160 - 45 = 115

Therefore, Mechanic 1 made $45 an hour, and Mechanic 2 made $115 an hour.

Side Note: If I was a mechanic, I would prefer to be Mechanic 2 :-)

Answer 3

Classic systems of equations problem.

let x be the rate of one mechanic and y be the rate of the other mechanic:

so, x+y=160

Then you can use the length of time each work to create another equation to get the total cost:

so, 20x+15y = 2625.

I generally prefer the elimination method, when you stack the equations and eliminate one of the variable to solve for the other. You could also use the substitution method, in one equation solve for one variable and then plug that into the other equation.

If you have any follow up questions, just leave a comment.