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    algebra word problem

    A manufacturer wishes to make tee-shirts for the band Indigo Girls. They sell for $18 each. She must deliver all the tee-shirts in 20 days time. The manufacturer will first set up some machines. Once all machines are set up she will turn them on. Each machine takes one day to set up. A machine produces 200 shirts in one day. All the machines must be set up before any of them are turned on. Express the total amount of money M she will receive for the shirts in terms of the number n of machines she decides to set up (assuming she sells all the shirts she makes).
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    Quote Originally Posted by lilikoipssn View Post
    A manufacturer wishes to make tee-shirts for the band Indigo Girls. They sell for $18 each. She must deliver all the tee-shirts in 20 days time. The manufacturer will first set up some machines. Once all machines are set up she will turn them on. Each machine takes one day to set up. A machine produces 200 shirts in one day. All the machines must be set up before any of them are turned on. Express the total amount of money M she will receive for the shirts in terms of the number n of machines she decides to set up (assuming she sells all the shirts she makes).
    Let's assume that the delivery takes no day... That is to say that the shirts produced the 20th day can be delivered at once.

    If n is the number of machines that are set up, this means that there are n days over 20 due to the setup.
    Hence, there are 20-n days left to the n machines to produce their shirts. Let X be the number of t-shirts produced.

    There are n machines working during 20-n days to produce 200 shirts per day. Therefore : X=n(20-n)\cdot 200

    Since each shirt is sold 18$,

    \boxed{M=18 \cdot 200 \cdot n \cdot (20-n)}

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