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  1. #1
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    word problem help

    Find 2 numbers whose sum is 55 and whose product is 684 (show your work)






    What are the dimension of a rectangle if it's perimeter is 18.5 and it's area is 21 (show your work)
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  2. #2
    Super Member angel.white's Avatar
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    Quote Originally Posted by gumi View Post
    Find 2 numbers whose sum is 55 and whose product is 684 (show your work)
    Let A be the first number and B be the second number.

    then A+B = 55 and A*B = 684

    Solve for one variable
    A = 55-B

    Substitute it's value into the other equation so that you only have one variable in the other equation
    (55-B)*B = 684

    Set equal to zero so that quadratic formula can be used
    -B^2 -55B -684 = 0

    Use the quadratic formula The Quadratic Formula Explained to solve for B, and then plug that back into either equation to solve for A
    Last edited by angel.white; April 13th 2008 at 10:44 AM.
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  3. #3
    Moo
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    Hello,

    We can also see that 684=2^2 . 3^2 . 19

    A & B divide 684, so they divide 2.3.19 and their product is exactly 2.3.19

    All possible couples are :

    If a is the first factor, the second has to be 684/a as their product is 684
    (1 , 684)
    (2 , 2.3.19=342)
    (3 , 2.3.19=226)
    (4 , ...

    Wait, wait ! This is too long to do !!!!

    We know that A+B=55. So A & B are inferior to 55 ! Phew ! That reduces a lot the possibilities !
    Actually, the only one for which the two factors are inferior to 55 is this one :

    (2.3=36 , 19) -> WOW their sum is 55 !




    Did you understand how i got the couples ?
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  4. #4
    Super Member angel.white's Avatar
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    Quote Originally Posted by Moo View Post
    Did you understand how i got the couples ?
    Yes, I just wasn't sure if the answer was going to have integers or even rational numbers as solutions.
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  5. #5
    Moo
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    Actually, i had no worry that you would understand ^^ (and neither did i know )
    I was just asking gumi
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  6. #6
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    got it guys thanks
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