Robert has a summer job as a lifegard at Fitness Connection pool. Robert gets pa

Question

Robert has a summer job as a lifegard at Fitness Connection pool. Robert gets paid $8.75 an hour. Robert can get paid overtime if he works 35 hours a week. Robert's overtime pay is an extra $2.25 an hour for every hour over 25 hours. Robert it not allowed to work more than 50 hours per week.

a) Write a piecewise function to represent Robert's pay salary as a lifeguard.

b) What is the domain of this function?

c) What is the range of this function?

d) How many hours did Robert work if his paycheck was $372.25?

PLEASE WRITE NEATLY. I POSTED THIS QUESTION YESTERDAY AND GOT A REPLY BUT COULD NOT READ THE PERSONS WRITING!

Explanation / Answer

Robert gets paid 8.75$ per hours
If he works more than 25 hours a week then for every hour his hourly pay os 8.75+2.25 = 11$
a) Robert's salary as a lifeguard if he works 't' hours a week is : 8.75 t if t<=25 and 8.75t+ 2.25 (t-25) if t>25
b) Robert isn't allowed to work for more than 50 hours per week so he can work for anytime betwee 0 hours (now work at all) and 50 hours; Thus domain for 't' variable is = [0,50]
c) Range is the amount of money he can possible earn, i.e. 8.75 t + 2.25 (t-25) all possible values
at t=0, total earning = 8.75*0 = 0;
if t= 50 (max possible time) then total earnings = 8.75*50 + 2.25 (50-25) = 437.5 + 56.25 = 493.75 $
Thus, range is [0, 493.75]

d) if paycheck was 372.25 (note than 372.25 > 8.75*25 which means he worked over time too)
372.25 = 8.75 t + 2.25 (t-25)
11t -56.25 = 372.25
11t = 428.5
t= 428.5/11 = 38.8545 hours

Thus, if total earning = 372.25 then Robert worked for 38.9545 hours in total in that week

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