# 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?

##### 1 Answer

Sep 24, 2015

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

#### Explanation:

Suppose the digits are

We are given:

#a + b = 12#

#10a + b = 18 + 10 b + a#

Since

Substitute that into

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

That is:

#9a+12 = 138-9a#

Add

#18a = 126#

Divide both sides by

#a = 126/18 = 7#

Then:

#b = 12 - a = 12 - 7 = 5#

So the original number is