The sum of the digits of a two-digit number is 9. If the digits are interchanged, the resulting number equals the original number plus the sum of the digits. Find the number.

45

Step-by-step explanation:

we know the number is two digits.

we know that the sum of the digits is 9

therefore, the only possible numebrs are:

18, 81

27, 72

36, 63

45, 54

we also know that the inverse of the digits is the original number plus nine

therefore, 18 and 81 are out

27 and 72 are out

36 and 63 are out

the only numbers left are 45 and 54.

since 45+9=54, the number is 45.