SOLUTION: A bricklayer and an eectrician together 90 hours working on a new house. If the bricklayer earns $12 per hour, the electrician earns $16 per hour, and the wner pays them a total of

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Question 112096: A bricklayer and an eectrician together 90 hours working on a new house. If the bricklayer earns $12 per hour, the electrician earns $16 per hour, and the wner 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):
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Let x = the number of hours worked by the bricklayer and y = the number of hours worked by the electrician.
The total number of hours worked together can be expressed by:
x+y = 90
The amount earned by the bricklayer can be expressed by:
x($12)
The amount earned by the electrician can be expressed by:
y($16)
So the total amount earned by both is:
x($12)+y($16) = $1350
Now we have two equations with two unknowns:
1) x+y = 90 Rewrite this as x = 90-y and substitute into equation 2) then solve for y.
2) 12x+16y = 1350
2a) 12(90-y)+16y = 1350 Simplify.
1080-12y+16y = 1350 Combine like-terms.
1080+4y = 1350 Subtract 1080 from both sides.
4y = 270 Divide both sides by 4.
y = 67.5
x = 90-y
x = 90-67.5
x = 22.5
So the bricklayer worked 22.5 hours and the electrician worked 67.5 hours.
Check:
x+y = 90
22.5+67.5 = 90
90 = 90
$12x+$16y = $1350
$12(22.5)+$16(67.5) = $1350
$270 + $1080 = $1350
$1350 = $1350