Question

The sum of the digits of a two-digit number is 13. If 27 is added to the number, the digits will be interchanged. Find the number.

Answer 1

Hello from MrBillDoesMath!

Answer:

58

Discussion:

Suppose the 2-digit number is "ab". That is, 10a + b.

Sum of digits = 13  =>  a + b = 13   (*)

Digits reversed if 27 added to number  => (10a + b) + 27 = 10b + a  (**)

(**) =

(10a + b) + 27 = 10b + a            => subtract 10b, then a, from both sides

9a -9b = -27                              => divide both sides by 9

a - b = -3

From (*),  a+ b = 13 so  

(a-b) + ( a+b) = -3 + 13  =>

2a = 10 =>

a = 5

As  a +b = 13, 5 + b = 13 => b = 8

Hence the number "ab" is 58

Thank you,

MrB