Question

2 mechanics worked on a car. the 1st mechanic charged $75 per hour, and the 2nd charged $95. They worked a combined 20 hours and charged a total of $1800. How many hours did each mechanic work?

Answer 1

The first mechanic worked 5 hours and the second worked 15

Explanation:

Let h = hours for first mechanic

j = hours for second mechanic

h+j = 20

75h + 95 j = 1800

Multiply the first equation by -75

-75(h+j = 20)

-75h -75j = -1500

Add this to the second equation to eliminate h

75h + 95 j = 1800

-75h -75j = -1500

----------------------------

0 + 20j = 300

Divide by 20

20j/20 = 300/20

j = 15

Now gind h

h+j = 20

h +15 = 20

h = 5

Answer 2

1. set up the equations:

a. total cost: 75x + 95y = 1800

b. total hours: x + y = 20

2. use substitution:

a. x + y = 20 → x = 20 - y

3. plug in value of x:

a. 75(20 - y) + 95y = 1800

4. distribute (75).

1500 - 75y + 95y = 1800

5. combine like terms:

20y = 300

6. divide:

y = 15

7. plug in y to other equation to get x:

x + 15 = 20

8. solve:

x = 5

1st mechanic (x) worked 5 hours

2nd mechanic (y) worked 15 hours

hope this helps :)