Question

The sum of the digits in a two digit number is 11. If the digits are reversed, the new number will be 45 less than the original number. What is the original number?

Answer 1

t = 10's digit
u = 1's digit

t + u = 11
10u + t = 45 + (10t + u)

This second equation is the tricky part. It says that the VALUE of the reversed number (10 times the unit's digit added to the ten's digit itself) is equal to 45 more than the original number (10 times the ten's digit added to the unit's digit)

Combine like terms: 9u - 9t = 45
Solve by elimination:

9u - 9t = 45
-9u -9t = -99

-18t = -54

t = 3, u = 8

Original number is 38.