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.
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