SOLUTION: This is a word problem I am struggling with: You've been offered a part time job at a local retailer. You are being offered two different pay options: Plan A: $18 an hour with o

Question 26620: This is a word problem I am struggling with: You've been offered a part time job at a local retailer. You are being offered two different pay options:
Plan A: $18 an hour with overtime (above 20 hours/week) paying time and a half.
Plan B: $20 an hour with no over time.
I need to determine the algebraic formulas for plan A(x),(x being number of hours worked each week)and plan B(x) for a continuous domain of [0,40].
I have managed to figure out the plots for the graph but can't seem to wrap my head around the actual Algebraic formulas.
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
Plan A: $18 an hour with overtime (above 20 hours/week) paying time and a half.
OK LET HIM WORK FOR X HRS./WEEK
NORMAL RATE =18 $/HR.
O.T.RATE =18*1.5=27 $/HR.
NOW IN THE DOMAIN OF 0 TO 40,COMES THE 20HR/WEEK STANDARD AND BEYOND THAT O.T.RATE.
SO WE NEED TO DIVIDE THE DOMAIN INTO 2 PARTS.
1...0 TO 20 AND 2...>20 TO 40
SO NOW FOR X = 0 TO 20.WE HAVE PAY P AS
P=18X
AND FOR X>20..
WE HAVE NORMAL RATE HRS =20
AND EXCESS RATE HOURS =X-20
SO HIS TOTAL PAY P IS
P=20*18+27*(X-20)...
THIS IS KNOWN AS DEFINING A FUNCTION DIFFERENTLY FOR DIFFERENT ZONES OF DOMAIN.SO WE GOT ....
P=18X....FOR X=0 TO 20....AND
P=360+27(X-20)...FOR X>20...
I THINK NOW YOU CAN DO PLAN B BY YOUR SELF ON THIS BASIS.IF YOU HAVE DIFFICULTY COME BACK.
Plan B: $20 an hour with no over time.
I need to determine the algebraic formulas for plan A(x),(x being number of hours worked each week)and plan B(x) for a continuous domain of [0,40].

RELATED QUESTIONS
I've been struggling with this problem. 13n-12 ≤ -8+9n I don't know how to solve... (answered by CubeyThePenguin,josgarithmetic,ikleyn)

I have been struggling with a word problem. The problem is "Best rentals charges a daily (answered by math_tutor2020,ikleyn,josgarithmetic,MathTherapy)

Here is a difficult word problem I am struggling with: 8-year-old Samantha visited... (answered by Alan3354,stanbon)

This is a word problem involving ratios that I have been struggling with for a couple of... (answered by Earlsdon)

Could someone please help me? I am in need of a lesson on how to tackle algebra 2 word... (answered by ReadingBoosters)

Hi! I've been trying this problem for some time and I can't seem to figure it out. A... (answered by ikleyn,MathTherapy)

Julie has been offered a job for $400 per week. She has a second job offered for... (answered by rfer)

hello I am really struggling with this word problem: A high school student was able... (answered by stanbon)

Create a function with the following domain: x<-4. Thank you so much I have been... (answered by ikleyn)