Question

The sum of the digits of a two digit number is 12. When the digits are reversed the new number is 18 less than the original number. How do you find the original number?

Answer 1

Express as two equations in the digits and solve to find original number `75`.

Explanation:

Suppose the digits are `a` and `b`.

We are given:

`a + b = 12`

`10a + b = 18 + 10 b + a`

Since `a+b = 12` we know `b = 12 - a`

Substitute that into `10 a + b = 18 + 10 b + a` to get:

`10 a + (12 - a) = 18 + 10 (12 - a) + a`

That is:

`9a+12 = 138-9a`

Add `9a - 12` to both sides to get:

`18a = 126`

Divide both sides by `18` to get:

`a = 126/18 = 7`

Then:

`b = 12 - a = 12 - 7 = 5`

So the original number is `75`