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Math Help - Having trouble

  1. #1
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    Having trouble

    Here is my problem:
    Find 4 consecutive odd integers where the product of the two smaller numbers is 64 less than the product of the two larger numbers.
    I have many like that and I can't figure them out for anything... I tried searching the web but no luck.

    Any help is GREATLY appreciated.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Ryuuko View Post
    Here is my problem:

    Find 4 consecutive odd integers where the product of the two smaller numbers is 64 less than the product of the two larger numbers.
    I have many like that and I can't figure them out for anything... I tried searching the web but no luck.

    Any help is GREATLY appreciated.
    let the smallest be n, then the integers are n, n+1, n+2 and n+3.

    The product of the two smallest is n(n+1), and of the two largest is
    (n+2)(n+3), so we are told that

    n(n+1) = (n+1)(n+3) - 64.

    Which is a quadratic in n, you solve this then you have your four numbers.

    RonL

    Oppsss.. odd integers.. anyway you get the idea
    Last edited by CaptainBlack; June 6th 2007 at 01:44 PM.
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  3. #3
    Super Member

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    Hello, Ryuuko!

    Find 4 consecutive odd integers where the product of the two smaller numbers
    is 64 less than the product of the two larger numbers.

    You're expected to know how to express consecutive odd integers.

    Since odd integers "go up by two", if x is the first one,
    . . then the next three are: . x + 2,\:x + 4,\:x + 6


    \underbrace{\text{Product of smaller two}}\;\;\underbrace{\text{is}}\;\;\underbrace{\te  xt{ 64 less than product of larger two}}

    . . . . x(x + 2) . . . . . . = . . . . . (x + 4)(x + 6) - 64


    There is our equation! . . . Can you finish it now?

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