algebra word prob. - one more

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The sum of the digits of a certain two-digit number is 7. Reversing its digits increases the number by 9.
What is the number?

TIA

  • algebra word prob. - one more -

    [ab] = 10 a + b
    a+b = 7
    [ba] = 10 b + a = 9 + 10a + b
    two equations

    a + b = 7
    and
    10 b + a = 9 + 10 a + b
    9 b = 9 + 9 a
    b = 1 + a
    combine
    a + b - b = 7 - 1 - a
    2 a = 6
    a = 3
    then b = 4
    so answer is
    34

    check
    34 + 9 = 43 sure enough

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