Question

If the unit’s digit of a two-digit number is 6 more than the ten’s digit and the number is 8 more than twice the sum of the digits, what is the number?

Answer 1

Let t=ten's digit, and u=unit's digit,
Consider the digits:
u=t+6 ..... (1)
Consider the number:
t*10+u = 2*(t+u)+8 (2)

Substitute u from (1) into (2)
10t+(t+6)=2(t+t+6)+8

Solve for t and back-substitute in (1) to find u.
(Answer check: the two digit number has 7 as a factor.)