Question 142968: Any help with this system of linear equations will be appreciated.
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?
Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! Let x = number of hours spent by the bricklayer.
Let y = number of hours spent by the electrician.
From the problem description, you can write:
1) x+y = 90 "A bricklayer and an electrician together spend 90 hours..."
2) $12(x) + $16(y) = $1350 "...the owner pays them a total of $1350 for their work,..."
Rewrite equation 1) as: x = 90-y and substitute into equation 2).
2a) 12(90-y) + 16y = 1350 Simplify and solve for y.
2a) 1080-12y + 16y = 1350
2a) 1080 + 4y = 1350 Subtrct 1080 from both sides.
2a) 4y = 270 Divide both sides by 4.
2a) y = 67.5
x = 90-y
x = 90-67.5
x = 22.5
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The bricklayer spent 22.5 hours on the house.
The electrician spent 67.5 hours on the house.
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