Question

When you reverse the digits in a certain two digit number you increase its value by 18. what is the number if the sum of its digits is 8?

Answer 1

ba=ab+18
a+b=8, b=8-a

10b+a=10a+b+18
10b-b=10a-a+18
9b=9a+18
9(8-a)=9a+18
72-9a=9a+18
9a+9a=72-18
18a=54
a=54:18
a=3
b=8-3
b=5
the number is 35
check 53=35+18
           53=53    true