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    Topics || Problems

    In an integer between 10 and 100, the units' digit is 3 greater than the tens' digit. Find the integer if it is 4 times as large as the sum of its digits.
    Solution:

    Let x be the units' digit and y be the tens' digit. Thus the number is 10y + x.

    The units digit is 3 greater than the tens' digit: x = 3 + y (1)

    The integer is 4 times as large as the sum of its digits: 4(x+y) = 10y + x (2)

    Substitute 1 to 2: 4(3 + y + y ) = 10y +3 + y

    4(3 +2y ) = 11y +3

    12 + 8 y = 11y +3

    y = 3

    x = 3 + 3 = 6

    Thus the integer is 10(3) + 6 = 36