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algebra

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The sum of the digits of a certain two-digit number is 7. Reversing its digits increase the number by 9. What is the number. Use x and y. Please help me!!!!

  • algebra -

    in the original number, let the unit digit be x, then tens digiti be y

    so the original number is 10y + x
    where x+y = 7

    the number reversed will be 10x + y

    new number - old number = 9
    10x + y - (10y + x) = 9
    9x - 9y = 9
    or x-y = 1

    x+y=7
    x-y=1
    add them
    2x = 8
    x = 4, then y = 3

    the number is 10y+x = 34

    check:
    original number is 34
    reversed number is 43
    is the number increased by 9 ??? YES
    is the sum of the digits 7 ??? YES
    YEAHHH

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