how many positive two-digit integers are 27 more than the sum of their digits?

Question

how many positive two-digit integers are 27 more than the sum of their digits?

Answer 1

Let the number have the decimal representation AB.

 

It's value is 10A+B

 

The clue gives

 

10A + B = A + B + 27

 

9A = 27

 

A = 3

 

10·3 + B = 3 + B + 27

 

30 + B = B + 30

 

B is any digit.

 

Thus there are ten such numbers: 30,31,...,39.