Value mixture problem

Question

Two mechanics worked on a car. The first mechanic charged 75$ per hour, and the second mechanic charged 70$ per hour. The mechanics worked for a combined total of 20 hours, and together they charged a total of $1475. How long did each mechanic work?

Answer 1

Let x be the number of hours the mechanic (A) who charges $70 and hour works.

Let y be the number of hours the mechanic (B) who charges $75 and hour works.

Together they work 20 hours so: x + y = 20. (equation 1)

70*x is the amount of money mechanic A makes.

75*y is the amount of money mechanic B makes.

Together they make $1475 so: 70*x + 75*y = 1475 (equation 2)

You know have two equations in two unknowns which you can solve to determine x and y.

Answer 2

Hey Kalyn. It looks like in this problem you have two items you do not know. They are the hours worked by the two mechanics. In order to solve this you will need to create an equation that matches all the data. So here's an equation that tells you what you know about their hours worked with A as mechanic 1 and B as mechanic 2

A + B=20

75A+70B=1475

Now you need to begin simplifying. So, what you can do is multiply all the variables in the first equation by -75. Now you have

-75A -75B=-1500 (20x-75)

75A + 70B=1475

Now put the two equations together.

The A cancels out. The B becomes -5B and the other side becomes -25

So your equations looks like this

-5B=-25

Divide by -5 to get just B.

Your answer is B=5.

20-5=15 thus mechanic A worked 15 hours and mechanic B worked 5. You can check this by multiplying 70x5 and adding 75x15 to get a total of 1475

Hope that helps!