# The sum of the digits of a two-digit number is 10. If the digits are reversed, a new number is formed. The new number is one less than twice the original number. How do you find the original number?

##### 1 Answer

May 21, 2018

Original number was

#### Explanation:

Let

We are told that:

Now. to form the new number we must reverse the digits. Since we can assume both numbers to be decimal, the value of the original number is

and the new number is:

We are also told that the new number is twice the original number minus 1.

Combining [B] and [C]

Replacing [A] in [D]

Since

Hence the original number was:

Check: New number