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Word Problems/price-wise function

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Question
Assume you work at a company where you are paid hourly. You are paid $7.80 per hour for regular time (less than or equal to thirty-five hours) and time and three-quarters for overtime hours up to forty-five hours in one week. If you are asked to work forty-five or more hours in one week you are paid double-overtime. Write this information in the form of a piecewise-defined function and be sure to include the domain for each piece. Also, check your model by calculating the pay for working thirty-five hours and for working thirty-six hours. Post these values as well.

Answer
Hello Ashley,

Let x=the number of hrs worked per week, and w(x)=weekly pay (in $'s)...

for 0<=x<=35, w(x)=7.80x
for 35<x<45, w(x)=7.80*35+7.80(1+3/4)(x-35)=13.65x-204.75
for x>=45, w(x)7.80*35+7.80(1+3/4)*10+7.80*2(x-45)=15.6x-292.5

Check:
x=35 ==> w(35)=7.80*35=273
x=36 ==> w(36)=13.65*36+-204.75=286.62
x=46 ==> w(46)=15.6*46-292.5=425.10

I hope this helps.

Abe

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Abe Mantell

Expertise

Hello, I am a college professor of mathematics and regularly teach all levels from elementary mathematics through differential equations, and would be happy to assist anyone with such questions!

Experience

Over 15 years teaching at the college level.

Organizations
NCTM, NYSMATYC, AMATYC, MAA, NYSUT, AFT.

Education/Credentials
B.S. in Mathematics from Rensselaer Polytechnic Institute
M.S. (and A.B.D.) in Applied Mathematics from SUNY @ Stony Brook

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