SOLUTION: A T-shirt company will place custom logos on shirts. A group must order a minimum of 100 T-shirts to get the price per shirt of $12. But a discount is offered for larger orders. Fo

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Question 763495: A T-shirt company will place custom logos on shirts. A group must order a minimum of 100 T-shirts to get the price per shirt of $12. But a discount is offered for larger orders. For each set of 10 more shirts, the price of each shirt will decrease by $0.50.
a. Assuming that a group must place a minimum order of 100 shirts, find the equation that models the total cost C(t) for the T-shirts. (Hint: Define t to be the number of sets of 10 T-shirts ordered beyond 100, i.e. t = 2 if 20 more T-shirts are ordered)
Find the equation that models this situation
b. Use the model to find the cost for buying 200 T-shirts.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
(a)
The group ordered at least 100 T-shirts at $12/ shirt
+100%2A12+=+1200+
Let +t+ = number of sets of 10 t-shirts beyond 100
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+.5t+ is the discount for sets of 10 t-shirts beyond 100
+120t+ is the cost for a set of 10 t-shirts without the discount
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+C%28t%29+=+1200+%2B+120t+-+.5t+
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(b)
For 200 -shirts:
( note that +t+=+100+%2F+10+ )
+C%28+10+%29+=+1200+%2B120%2A10+-+.5%2A10+
+C%28+10+%29+=+1200+%2B+1200+-+5+
+C%28+10+%29+=+2400+-+5+
+C%28+10+%29+=+2395+
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Hope I got it