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Math Help - Numerals puzzle

  1. #1
    Member Rimas's Avatar
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    Numerals puzzle

    A positive number can be represented by a two digit numeral. If five times the sum of its digits is added to the number the digits are reversed what is the number?
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Rimas View Post
    A positive number can be represented by a two digit numeral. If five times the sum of its digits is added to the number the digits are reversed what is the number?
    Let the two digit number be "xy" that is to say 10*x + y
    So
    5(x + y) + (x*10 + y) = (10*y + x)

    5x + 5y + 10x + y = 10y + x

    14x = 4y

    7x = 2y

    Now, each of x and y must be an integer between 0 and 9 inclusive. Thus 2y is an integer no greater than 18. Thus x may only be 1 or 2. (If x = 0 then y = 0, but "xy" is supposed to be a two digit number and "00" is technically not a two digit number.)

    So if x = 1:
    7 = 2y ==> y is not an integer.

    If x = 2:
    14 = 2y ==> y = 7

    So your number is 27.
    5*(2 + 7) + 27 = 5*9 + 27 = 45 + 27 = 72 (Check!)

    -Dan
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