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Question 855198: A Studentt started a business. He bought a lawn mover for $745.He decided to hire a man at 7$ per hour to operate the lawn mover while he knocked on doors to drum up business.It costs $4 hour to run the lawn mover with gas and oil.The student charges 20$ an hour for moving the lawn.
How many hours mustt the lawn mover be operated before the student breaks even?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! cost function is:
c = 745 + 7x + 4x which is equal to 745 + 11x
revenue function is:
r = 20x
x is the number of hours.
to break even, these functions need to be equal to each other.
you get:
20x = 745 + 11x
subtract 11x from both sides of this equation to get:
9x = 745
divide both sides of this equation by 9 to get:
x = 745/9
that's your break even point.
it is equivalent to 82.78 hours rounded to 2 decimal places.
when x = 745/9, r = 20x = 14900 / 9
when x = 745/9, c = 745 + 11x = 745 + 8195 / 9
this is equivalent to (745 * 9 + 8195) which is equal to 14900 / 9.
since r = c, this is the break even point.
when x is greater than 745/9, he will make some profit.
for example, when x = 83 hours:
r = 20*83 = 1660
c = 745 + 11*83 = 1650.
he will have made a profit of 10 dollars.
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