A plumber, electrician and painter were all hired to work on 3 different house. For Adam's house, a plumber worked a total of 35 hours, an electrician worked 42 hours and a painter needed 29 hrs to complete the job. the total cost of the three workers for adam's house was $2,570.

Question

A second house they worked on was the watson home. in this house each of the three workers needed 28 hours to complete their part of the job. The total cost of the work on the watson home was $1,960.

A third house belonged to the Miller family. The electrician worked 24 hours, the plumber 30 hours and the painter worked 25 hours. the total for this home was $1,845.
** Using the information from these three homes, how much did each of the workers charge per hour?

Please help I don't know how to solve this question

Answer 1

First set up equation for each house to put together a system of 3 linear equations.
You can then solve by the method you have learned.
Finally post your answer for checking as necessary.

I will start the setting up of the equations.

Let
M=pluMber's hours
E=electrician's hours
N=paiNter's hours

For Adam's house:
35M+42E+29N=2570 ...(1) Adam's house
28M+28E+28N=1960 but can be simplified to
M+E+N=70 ...(2) Watson's house
30M+24E+25N=1845 ...(3) Miller's home
Note that the order is different in Miller's home, but rearranged to the same initial order.

The system of equations to be solved will then be:
35M+42E+29N=2570 ...(1)
M+E+N=70 ...........(2)
30M+24E+25N=1845 ...(3)

You can solve the system of equations using the method(s) you have learned, such as Gauss elimination, Cramer's rule, iterations, etc.
Post your answer for a check if you wish, or you can substitute the solution into each equation to check.

Answer 2

When I solved the system of equations I got M=25, E=30 and N=15 and when I substituted into each equation it worked, thank you so much!