SOLUTION: A T-shirt shop charges $18 per shirt for orders of 32 shirts or fewer. Once an order exceeds 32 shirts, the price drops to $17.5 for each additional shirt order. Write a piecewise

Question 1088031: A T-shirt shop charges $18 per shirt for orders of 32 shirts or fewer. Once an order exceeds 32 shirts, the price drops to $17.5 for each additional shirt order. Write a piecewised defined function C to represent the total cost of an order based on the number of shirts x. C(x)=_____if x <= 32 C(x)=_____if x>32
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

x = number of shirts ordered

A T-shirt shop charges $18 per shirt for orders of 32 shirts or fewer. means C(x) = 18x if x <= 32

Once an order exceeds 32 shirts, the price drops to $17.5 for each additional shirt order. means C(x) = 17.50(x-32)+576 if x > 32.

The "576" comes from the fact that 32*18 = 576. This is the total amount spent from buying the first 32 shirts (at $18 a shirt). This is the largest amount you can spend for the first piece of the piecewise function.

The portion 17.50(x-32) represents the added cost of buying some additional number of shirts over 32. For example, if x = 35, then x-32 = 35-32 = 3 additional shirts are bought at 17.50, meaning the cost for this portion is 17.50*(x-32) = 17.50*3 = 52.50 which is added onto the 576 to get the total cost for buying 35 shirts.

RELATED QUESTIONS
A T-shirt company charges $15 per shirt and offers a $200 rebate for orders greater than... (answered by josmiceli)

(piecewise function) You have a big extended family, and every Christmas you are... (answered by josgarithmetic)

A T-shirt company will place custom logos on shirts. A group must order a minimum of 100... (answered by josmiceli)

t shirts r us gives quote of $24 set up fee and $3 per shirt. shirts n things has no set... (answered by macston)

12. For a school band trip, Marcia decides to order T-shirts for all of the participants. (answered by ankor@dixie-net.com)

Solve Problems Using Linear Systems 12. For a school band trip, Marcia decides to order... (answered by Alan3354)

My problem is as follows: I need to write a function of the total amount of payment (P)... (answered by rothauserc,MathTherapy)

Jenny is in charge of ordering T-shirts for the math club at her school. If she paid $240 (answered by Boreal)

The student council is having t shirts printed. D shirtworks charges $200 plus $3.50 per... (answered by rfer,josmiceli)