The sum of the digits of a two-digit counting number was 13. When the digits were reversed, the new number was 9 less than the original number. What was the original number?

So the number is xy (this doesn't mean x times y)

x+y=13

yx=xy-9

the digits cannot be the same

they must add up to 13 so they cannot be positive so the number pairs are single digits so

9+4

8+5

7+6

the possible numbers pairs are

94 and 49

85 and 58

76 and 67

we find the differences

94-49 = greater than 9

85-58 = greater than 9

76-67=9

the original number is 76