t = the tens digit
u = the units digit
10t+u = the number
t+u = sum of digits
The units digit of a two-digit number is 2 more than the tens digit.
So u = t+2
If the number is divided by the sum of its digits, the partial quotient is 4 and the remainder is 3.
We divide as below. Multiply the partial quotient 4
by the divisor, t+u, getting 4t+4u. Then subtract that
from the dividend, 10t+u, and get remainder 6t-3u:
4
t+u)10t+ u
4t+4u
6t-3u = Remainder
And we are given that the remainder is 3. So
6t-3u = 3
So we have to solve this system of equations:
u = t+2
6t-3u = 3
Solve that by substitution and get t = 3 and u = 5.
So the number is 35.
Edwin