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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.
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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
Solved and thoroughly explained.