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Question 5278: Mr.Ranger is a plumber. He bills his clients for the cost of the call plus the number of hours he works. He earns $470 for a job that takes him 12 hours, whereas he recieves $225 for a 5 hour job.
a) what is his hourly rate?
b)what does he charge for the call?
c)Give an equation that represents his earnings.
d)Mr.Ranger has jsut finished a contract for which he will be paid $295. How many hours did he work?
Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! Since you are looking for two unknowns (x = cost of call and y = hourly rate), it seems reasonable to expect to require two equations to solve the problem.
Let's set up the required equations from the given information:
1) x + 12y = $470 The cost of the call (x) + 12 hrs @ $y per hour is $470.
2) x + 5y = $225 The cost of the call (x) + 5 hrs @ $y per hour is $225.
Rewrite equation 1): x = $470 - 12y and substitute into equation 2).
2a) ($470 - 12y) + 5y = $225 Simplify and solve for y, the hourly rate.
$470 - 7y = $225 Subtract $225 from both sides.
$245 - 7y = 0 Add 7y to both sides.
$245 = 7y Divide both sides by 7.
$35 = y This is Mr. Ranger's hourly rate.
To find the cost of the call, x:
x = $470 - 12y
x = $470 - 12($35)
x = $470 - $420
x = $50 This is Mr. Ranger's cost of the call.
The equation that represents his earnings can now be written as:
E = $50 + $35(y) Where: y is the number of hours spent doing the job.
Verification is left as an exercise for the student.
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