SOLUTION: The unit digit of a two digit number is 1 less than the tens digit. If the number is increased by 8 and then divided by the sum of the digits, the result is 8. Find the number.

Let the "tens" digit be t.

Then the "units" difit is (t-1), according to the condition.


Hence, the number itself is  N = 10t + (t-1).


Then the number N+8 is  10t + (t-1) + 8 = 10t + t + 7 = 11t + 7.


From the last statement of the problem, we have this equation


    N+8 = 8*(t+u),

or

    11t + 7 = 8*(t+(t-1)).


Simplify and find t


    11t + 7 = 8*(2t-1)

    11t + 7 = 16t - 8

      7 + 8 = 16t - 11t

       15   =    5t

        t   =    15/5 = 3.


Thus the tens digit is 3;  the units digit is 3-1 = 2;  and the number itself is  32.    ANSWER