The digits of a two-digit number sum to 8. When the digits are reversed, the resulting number is 18 less than the original

number. What is the original number?

It's 53.

Step-by-step explanation:

Let the number be xy so the digits are x and y, so:

x + y = 8 ... (1)

Reversing the 2 digits we have the number 10y + x and this equals

10x + y - 18 so we have the equation:-

10x + y - 18 = 10y + x

9x - 9y = 18

x - y = 2 ... (2) Adding equations (1) and (2) we have:

2x = 10

x = 5

and y = 8 - 5 = 3.

So the original number is 53.

We can check this as follows

Original number is 53 so the reverse is 35.

53 - 35 = 18 which checks out.