Question 395146
The solution to the first problem provided by another tutor is correct. The solution to the second problem has an error.<br>
2. the units digit of a two-digit number is 3 less than its tens digit. if the number is divided by the sum of its digits, the quotient is 6 and the remainder is 8. find the number.

The proper equations which express this are:
u = t-3
{{{(10t+u)/(t+u) = 6 + 8/(t+u)}}}<br>
We can eliminate the fractions in the second equation if we multiply both sides of the equation by (t+u):
{{{((10t+u)/(t+u))(t+u) = (6 + 8/(t+u))(t+u)}}}
which simplifies as follows:
10t + u = 6*(t+u) + 8
10t + u = 6t + 6u + 8
Substituting t-3 for u we get:
10t + (t-3) = 6t + 6(t-3) + 8
which simplifies to:
11t - 3 = 6t + 6t - 18 + 8
11t - 3 = 12t - 10
Subtracting 11t from each side:
-3 = t - 10
Adding 10 to each side:
7 = t
This makes u = 7-3 or 4.
The original number is 74.