A bricklayer and an electrician together spend 90 hours working on a new house. If the bricklayer earns $12 per hour, the electrician earns $16 an hour, and the owner pays them a total of $1350 for their work, how many hours does each worker spend on the house?

Let's say that the bricklayer works for x hrs and the electrician works for y hrs.

A bricklayer and an electrician together spend 90 hours  --- (x+y) = 90

Bricklayer earns $12/hr  ----  so he earns $12x altogether. (he works for x hrs)

Electrician earns $16/hr ---- so he earns $16y altogether (he works for y hrs)

Altogether, they get paid $1350  ---- Hence, (12x + 16y) = 1350

We now have a pair of simultaneous equations:

(x+y) = 90.....(1)
(12x + 16y) = 1350....(2)

Manipulate (1):  x = 90-y...(3)

Substitute (3) into (2)

12(90-y) + 16y = 1350

1080 - 12y + 16y = 1350

4y = 270

y = 67.5 hrs ....(4)

Substitue (4) into (3)

x = 90 - 67.5 = 22.5hrs

Hence, the bricklayer worked for 22.5hrs and the electrician worked for 67.5hrs.