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Math Help - [SOLVED] Difficult Problem..

  1. #1
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    [SOLVED] Difficult Problem..

    Hi i have a "challenge" problem that i have to solve. I have no idea how i should write the equation to solve this. I don't understand how I can make an equation to answer both parts of the question. Should i use 2 variables? One for price and one for the number of magnets produced? Please take a look.

    The question is: your company makes fridge magnets. The materials for each magnet is $0.14. Your company has additional expenses of $27 000 year. The per-magnet cost is \frac{total-costs-per-year}{number-produced-per -year}. If your company can make and sell twice as many magnets next year as this year, the per-magnet cost will be reduced by $0.90. How many magnets is your company making and selling this year?

    Thanks.
    Last edited by demo1; February 24th 2009 at 05:16 PM.
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  2. #2
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    Quote Originally Posted by demo1 View Post
    The question is: your company makes fridge magnets. The materials for each magnet is $0.14. Your company has additional expenses of $27 000 year. The per-magnet cost is \frac{total-costs-per-year}{number-produced-per -year}.
    Okay, let the number of magnets being made this year be n. The current cost per-magnet is

    \frac{27\,000+0.14n}n.

    If your company can make and sell twice as many magnets next year as this year, the per-magnet cost will be reduced by $0.90.
    The cost for next year would be

    \frac{27\,000+0.28n}{2n}

    which is $0.90 less than the current year. Hence,

    \frac{27\,000+0.28n}{2n}=\frac{27\,000+0.14n}n-0.9.

    Multiply through by n,

    13\,500+0.14n=27\,000+0.14n-0.9n

    \Rightarrow0.9n=13\,500

    \Rightarrow n=15\,000.
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  3. #3
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    Wow THANKS! That was more simple than i anticipated.
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