SOLUTION: For a recent job, a plumber earned $28/h, and the plumber's apprentice earned $15/h. The plumber worked 3 hours more than the apprentice. If together they were paid $213, how muc

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Question 162334This question is from textbook Algebra and Trigonometry
: For a recent job, a plumber earned $28/h, and the plumber's apprentice earned $15/h. The plumber worked 3 hours more than the apprentice. If together they were paid $213, how much did each earn? This question is from textbook Algebra and Trigonometry

Found 2 solutions by checkley77, gonzo:
Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
28(T+3)+15T=213
28T+84+15T=213
43T=213-84
43T=129
T=129/43
T=3 HOURS FOR THE APPRENTICE.
3+3=6 HOURS FOR THE PLUMBER.
PROOF:
28*6+15*3=213
168+45=213
213=213

Answer by gonzo(654) About Me  (Show Source):
You can put this solution on YOUR website!
let P = number of hours that the plumber worked.
let H = number of hours that the helper worked.
since the plumber worked 3 more hours than the helper, the equation for hours worked is
P = H + 3
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since the plumber earned 28 dollars per hour and the helper earned 15 dollars per hour, the equation for amount of money each made is the number of hours each worked times the dollars per hour each earned.
this equation is
(28*P) + (15*H) = 213 dollars
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couple of ways to solve this.
both get the same answer.
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first way
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substitute for P in the money equation since P is the same as H + 3.
equation becomes
(28*(H+3)) + (15*H) = 213
solve for H.
28*H + 28*3 + 15*H = 213
43*H + 84 = 213
43*H = 129
H = 3
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if H = 3, then P = 6 because P = H + 3.
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6*28 + 3*15 = 213 so your answer is
Plumber works 6 hours
Helper works 3 hours.
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the other way to solve this is to make both equations in the same form and then solve them simultaneously as follows
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P = H + 3 is transformed to become
P - H = 3
you need to solve
P - H = 3
and
28*P + 15*H = 213
simultaneously.
multiply the P - H equation by 28 so you can remove one of the unknowns.
your equations become
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28*P - 28*H = 28*3
28*P + 15*H = 213
subtracting the top equation from the bottom equation and you get
0*P + 43*H = 213 - 84 equals
43*H = 129
which becomes
H = 3
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you get the same answer once you solve for P as before.
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