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Math Help - A little bit of help is needed please!

  1. #1
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    A little bit of help is needed please!

    I have a problem that I answered using logic, but I can't get figure out the working for it.

    The question is:
    Solve using the five step method.
    When the digits of a two-digit number are reversed, the new number is 9 more than the original, and the sum of the digits of the original number is 11. What is the original number?

    My answer: 56

    My process: There are only a few numbers that add up to 11: 1+10, 2+9, 3+8, etc. However, only one of these pairs are consecutive, and only consecutive numbers behave as described in the question when reversed(e.g. 34 and 43, 67 and 76 and so on). Thus the answer is 56.

    Thanks in advance for your help.
    Drakmord
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by drakmord View Post
    I have a problem that I answered using logic, but I can't get figure out the working for it.

    The question is:
    Solve using the five step method.
    When the digits of a two-digit number are reversed, the new number is 9 more than the original, and the sum of the digits of the original number is 11. What is the original number?

    My answer: 56

    My process: There are only a few numbers that add up to 11: 1+10, 2+9, 3+8, etc. However, only one of these pairs are consecutive, and only consecutive numbers behave as described in the question when reversed(e.g. 34 and 43, 67 and 76 and so on). Thus the answer is 56.

    Thanks in advance for your help.
    Drakmord
    That looks great to me!
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  3. #3
    MHF Contributor

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    Quote Originally Posted by drakmord View Post
    I have a problem that I answered using logic, but I can't get figure out the working for it.

    The question is:
    Solve using the five step method.
    When the digits of a two-digit number are reversed, the new number is 9 more than the original, and the sum of the digits of the original number is 11. What is the original number?

    My answer: 56

    My process: There are only a few numbers that add up to 11: 1+10, 2+9, 3+8, etc. However, only one of these pairs are consecutive, and only consecutive numbers behave as described in the question when reversed(e.g. 34 and 43, 67 and 76 and so on). Thus the answer is 56.

    Thanks in advance for your help.
    Drakmord
    As Chris L T521 says, your answer is perfectly valid. I, not being able to think as clearly as you, need a crutch. I would argue:
    The two digit number, mn, means 10m+ n. With the digits reversed, that is 10n+ m and saying that is "9 more than the original" means 10n+ m= 10m+ n+ 9 or 9n- 9m= 9. n-m= 1. That tells me that n and m are consecutive numbers- that was so clear to you from the start! That is, n= m+1. The sum of the digits is 11 so m+ n= 11. Since n= m+1, m+ (m+1)= 2m+1= 11, 2m= 10, m= 5. n= m+1= 6. The number is, as you say, 56.
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