Question

The sum of a number of tow digits and of the number formed by reversing the digits is 110 and the difference of the digits is 6. Find the number

Answer 1

We can let the digits of the number be a and b.

First number:

10a+b

Second number (first number with digits reversed):

10b+a

The two of them sum to 110:

(10a+b)+(10b+a)=110

Difference of the digits is 6:

b=a+6

Plug everything in and solve:

(10a+(a+6))+(10(a+6)+a)=110

11a+11a+66=110

22a=44

a=2

b=a+6=2+6=8

Our numbers are 28 and 82. Quick check:

28+82=110✓