You get three summer jobs to help you save for college expenses. In your job as

Question

You get three summer jobs to help you save for college expenses. In your job as a cashier, you work 20 hours per week and earn $9.50 per hour. Your second and third jobs ar at the local hospital. There, you earn $9.00 per hour as a payroll clerk and $7.00 per hour as an aid. You always work 10 hours kess perweek as a aid that you do as a payrole clerk. Your total weekly salary depnds on the number if hours you work at each job.

a. Determine the input and output variables for this situation.

b. Expalin how you calculate the total amount erned each week.

c. If x repersents the number of hours you work as a payrole clerk, repersent the number of hours work as a aid in terms of x.

d. Write an equation that describes the total amount you earn each week. Use x to repersent the input variable and y repersents the output variable. Simplify the expression as much as possible.

e. If you wrok 12 hours as a payrole clerk, how much will you make in one week.

F. What are the practicale replacement values for x? Would 8 hours at your payroll job be a realistic replacement value? What about 50 hours?

g. When you don't work as an aid, what is your total weekly salary?

h. If you plan to earn a total of $505 in one week from all of te jobs, how many hours must you work at each job? Is the tatal number of hours worked realistic? Explain

i. Solve the equation in part d for x in terms of y. When would it be useful to have the equation in this form.

Explanation / Answer

Ans(a):

Input variable is "number of hours".

Output variable is "Total earning".

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Ans(b):

to find total earning we multiply pay rate and number of working hours of respective jobs then add all three payments.

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Ans(c):

9x

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Ans(d):

y=9.5(20) + 9x + 7(10)

or

y=190 + 9x + 70

or

y=9x+260

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Ans(e):

plug x=12

y=9x+260=9*12+260=$368

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Ans(f):

Practical replacable values of x are all positive numbers because number of hours can't be negative.

As possible working hours and sleeping hours are not defined so i'm not going to fix upper value of x.

Just remember that total hours (20+x working hours+ 10 + sleeping hours) can't exceed (7 days times 24 hours) a week.

using same logic, 8 hours at payrole job or 50 hours may be realistic if you are able to work too much without any tension.

otherwise working 50 hours may not be realistic due to stress.

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Ans(g):

Just remove calculation of aid.

so answer is

y=9.5(20) + 9x

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given earning is $505 that is y=505

plug into y=9x+260

505=9x+260

245=9x

x=245/9

which is approx 27.2 hours.

so total work hours in a week = 20 (cashier) +27.2 (payroll clerk) +10 (aid) =57.2

per day working hour =57.2/7=8.2

which can be easily covered per day so yes that is practically possible.

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Ans(i):

y=9x+260

or y-260=9x

or x=(y-260)/9

yes it is helpful to determine number of hours needed in payrole to get any particular earning.

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