Question 306765
The sum of the digits of a two digit counting number is 10. If the digits are reversed, the new number is two less than three times the original number. What is the original number?

Let x be the tens digit and y the units digit.

The original number then is 10*x + y. The new number is 10*y + x. 

We have then:

1.) x + y = 10 and
2.) 3*(10*x + y) - 2 = 10*y + x

From 1.) we have x = 10 - y.  Substituting 10 - y for x in 2.) we have:

3*(10*(10-y) + y) - 2 = 10*y + (10 - y)

3*(100 - 10y + y) - 2 = 10*y + (10 - y)
3*(100 - 9*y) - 2 = 10*y + (10 - y)
300 - 27*y - 2 = 10*y + 10 - y
298 - 27*y = 9*y + 10
36*y = 288
y = 8

Substituting 8 for y in 1.) above we have:

x + y = 10
x + 8 = 10
x = 2

The original number then is 28.