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Math Help - How do you make $1.00 with 21 coins?

  1. #1
    veltel
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    Question How do you make $1.00 with 21 coins?

    Help Me plase


    Thank you
    Last edited by Jameson; March 30th 2007 at 12:02 AM. Reason: link not necessary
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  2. #2
    Super Member malaygoel's Avatar
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    10*8 + 2*7 + 1*6=100
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  3. #3
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by malaygoel View Post
    10*8 + 2*7 + 1*6=100
    What coins are these?

    I don't have anything better than trial and error, but I'd set it up like this:
    Let there be q quarters, d dimes, n nickels, and p pennies. Then:
    100 (cents) = 25q + 10d + 5n + 1p

    and

    q + d + n + p = 21

    Solve the second equation for p:
    p = 21 - q - d - n

    and insert this value of p into the first equation:
    100 = 25q + 10d + 5n + (21 - q - d - n)

    79 = 24q + 9d + 4n

    I would start with the assumption there are 3 quarters (which almost certainly won't work), and work my way down. It could take a while without some more insight, which I'm afraid I can't offer you.

    -Dan
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  4. #4
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    I am not sure what coins are you using.

    If you have a lot of coints it becomes the Frobenius Coin Problem.
    Last edited by ThePerfectHacker; March 30th 2007 at 08:01 AM.
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  5. #5
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    Hello, veltel!

    We have: . Q + . D .+ . N + P .= . 21
    . . .and: .25Q + 10D + 5N + P .= .100

    Subtract: .24Q + 9D + 4N .= .79


    From here, I found four solutions:

    . . 2Q, 3D, 1N, 15P
    . . 1Q, 3D, 7N, 10P
    . . . . . 7D, 4N, 10P
    . . . . . 3D, 13N, 5P

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