The sum of the digits of a two-digit number is 5. If nine is subtracted from the number, the digits will be reversed. Find the number

Question

The sum of the digits of a two-digit number is 5. If nine is subtracted from the number, the digits will be reversed. Find the number

Answer 1

Let x = tens digit and let y = ones digit.

The number can be expressed as 10x + y (Example: 37 = 10(3) + 7)

x + y = 5

(10x + y) - 9 = 10y + x

x + y = 5

9x - 9y = 9

x + y = 5

x - y = 1

So, 2x = 6

x = 3 and y = 2

The number is 32.