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Math Help - Reverse Digit problem help

  1. #1
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    Reverse Digit problem help

    I need help on understanding and do a reverse digit problem.

    problem is:

    If you take two-digit number to make a second two-digit number, and add these numbers together, their sun will be 121. What is the original number??
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  2. #2
    MHF Contributor Bruno J.'s Avatar
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    First number is 10a+b
    Reverse the digits, you get 10b+a
    add the two to get 10(a+b)+(a+b)=11(a+b)=121

    so you must have a+b=11. Possible choices (up to reversing the digits) are 29,38,47,56.
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    Thanks for the answer and i understand how to do the problem now.
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  4. #4
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    I'm assuming that when you say you "take two-digit number to make a second two-digit number", you make the second number by reversing the digits.

    Let x be the first digit, and y be the second digit.

    Your first number is x + 10y, so your second number is 10x + y

    When you add the two numbers together you have

    (x + 10y) + (10x + y) = 10x + x + 10y + y = 11x + 11y = 11(x + y) = 121

    So x + y = 11

    Remember, x and y represent the digits, so they are single digit numbers.

    So, we have:
    x y
    2 9
    3 8
    4 7
    5 6
    6 5
    7 4
    8 3
    9 2

    i.e. 29 + 92 = 38 + 83 = 47 + 74 = 56 + 65 = 65 + 56 = 74 + 47 = 83 + 38 = 92 + 29 = 121
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