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Math Help - help with elimination/substitution important!!! Urgent.

  1. #1
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    help with elimination/substitution important!!! Urgent.

    The sum of the digits of a two-digit number is 9. If the number is doubled, then decreased by 36, the answer is the original number with the digits reversed. Find the answer.

    You have to solve this word problem using elimination. Please help.

    Any Ideas?
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  2. #2
    Newbie Matrix's Avatar
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    if it is by elimination it is easy.
    it can be 45, 63, 72, or 81 or 54, 36, 27, 18 all are adding to 9
    but the first one 45 if doubled will be 90 -36 = 54 which is the first number reversed. the other will not work, you can try.
    Last edited by Matrix; September 20th 2005 at 08:35 PM.
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  3. #3
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    The two digit number xy is 10x + y. So 2(10x+y)-36 = 10y+x: that is, 19x-36=8y. Now 19x-36 is a multiple of 8 and so a multiple of 4. But 36 is a multiple of 4, so x is a multiple of 4: that is. x=0,4 or 8. Only x=4 gives a sensible value for y, namely y=5.
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  4. #4
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    Thanks! to that last post, thanks also to the first post, but I didn't need the answer, I needed the equation.
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  5. #5
    Site Founder MathGuru's Avatar
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    Lightbulb you don't need an equation

    This kind of question is very difficult to put in equation form. but if the 2-digit number is 't,s' where t is the tens digit and s is the ones digit then:

    t+s=9
    2(10t+s) - 36 = 10s + t

    however you stated in your problem that you must use elimination.

    With elimination we do not use equations we logically look at all possibilities and eliminate.

    In this case 18, 27, 36, 45, 54, 63, 72, 81, and 90 are the only possible two digit numbers whos digits sum to 9.

    Now you can look at them individually to see if they satisfy the second rule and eliminate those which do not.
    Last edited by MathGuru; September 21st 2005 at 02:19 PM.
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