Question

7. Charlotte has a babysitting service and charges $12.50 per hour.

After Charlotte calculated her set-up and travel costs, she constructed
the cost equation C = 45 + 2.50h, where C represents
the cost in dollars per job and h represents the hours
Charlotte babysits for.
a. Write an equation that represents the revenue, R, earned by
Charlotte in terms of number of hours, h.
b. By solving the equations simultaneously, determine the number of hours Charlotte needs to babysit
to cover her costs (that is, the break-even point).
c. In one week, Charlotte had four babysitting jobs as shown in the table.
Babysitting job
Number of hours (h) 5.0 3.5 4.0
7.0
i. Determine whether Charlotte made a profit or loss for each individual babysitting job.
ii. Did Charlotte make a profit this week? Justify your answer using calculations.
d. Charlotte made a $50 profit on one job. Determine the total number of hours she babysat for.

Answer 1

Explanation:

Charlotte's revenue earned : R = 12.50h.....where R = revenue earned and h represents hrs worked

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break even point :

12.50h = 45 + 2.50h

12.50h - 2.50h = 45

10h = 45

h = 45/10

h = 4.5 <== she would have to work 4.5 hrs to break even

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revenue - expenses = profit / loss

for 5 hrs...h = 5 for 3.5 hrs

12.50(5) - (45 + 2.5(5)) = 12.50(3.5) - (45 + 2.5(3.5)) =

62.5 - (45 + 12.5) = 43.75 - (45 + 8.75) =

62.5 - 57.5 = $ 5 profit 43.75 - 53.75 = -10....$ 10 loss

for 4 hrs for 7 hrs

12.50(4) - (45 + 2.50(4)) = 12.50(7) - (45 + 2.50(7)) =

50 - (45 + 10) = 87.5 - (45 + 17.5) =

50 - 55 = - 5.....$ 5 loss 87.5 - 62.5 = $ 25 profit

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12.50h - (45 + 2.50h) = 50

12.50h - 45 - 2.50h = 50

10h - 45 = 50

10h = 50 + 45

10h = 95

h = 95/10

h = 9.5 <=== she would have to work 9.5 hrs to make a $ 50 profit