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# Word Problems/price-wise function

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.

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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Word Problems

Volunteer

#### 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