Question 157925: Please help me with this!!
A carpenter charges a set fee for each job in addition to his hourly charge.
If a carpenter bills a customer $150 for a job that takes him 3 hours and bills a second customer $180 for a 6 hour job, how much would he charge for a job that takes him 9 hours?
TIA!
Joanne
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! If a carpenter bills a customer $150 for a job that takes him 3 hours and bills a second customer $180 for a 6 hour job, how much would he charge for a job that takes him 9 hours?
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Let x = set fee
and y = hourly rate
.
Since we have two unknowns, we'll need to find two equations.
.
Equation 1:
from: "a carpenter bills a customer $150 for a job that takes him 3 hours"
x + 3y = 150
.
Equation 2:
from: "and bills a second customer $180 for a 6 hour job"
x + 6y = 180
.
Subtract equation 1 from equation 2:
x + 6y = 180
-x - 3y = -150
----------------
3y = 30
y = $10/hour (rate)
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To find x, substitute the above into equation 1 and solve for y:
x + 3y = 150
x + 3(10) = 150
x + 30 = 150
x = $120 (set fee)
.
Our equation for cost is:
f(x) = 10x + 120
where x is the number of hours on the job
To calculate for a 9-hour job:
f(x) = 10x + 120
f(9) = 10(9) + 120
f(9) = 90 + 120
f(9) = $210
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