Electrician problem: An electrician, a carpenter, and a plumber are hired to work on a house. The electrician ?

Let x, y, and z represent number of hrs the electrician, carpenter and plumber worked, respectively.

24x+21.5y+25z=425

x+y+z=18

x-y=-2 (the carpenter,y, worked 2 more hrs than the electrician, x. So, x-y=-2)

Set up a matrix and use your calculator or the Gauss-Jordan elimination method. I opt for the calculator.

24...21.5...25...425

1.....1........1.....18

1......-1......0......-2

This matrix can be used to find the solution.

in row-reduced form you have:

1.....0......0.....4

0.....1......0.....6

0.....0......1.....8

So, x=4,y=6 and z=8

or, Electrician worked 4 hrs

Carpenter worked 6 hrs

Plumber worked 8 hrs

x= electrician hours

x+2= carpenter hours

18-(x+x+2) =16-2x=plumber hours

24x +21.5(x+2) + 25(16-2x) =425

24x +21.5x +43 +400 -50x =425

-4.5x = -18

x= 4 electrician hours

x+2=6 carpenter hours

8 plumber hours

717