We can think of the number as $$10a+b$$, where $$a$$ and $$b$$ are digits. Since the number is equal to the product of the digits $$(a\cdot b)$$ plus the sum of the digits $$(a+b)$$, we can say that $$10a+b=a\cdot b+a+b$$. We can simplify this to $$10a=a\cdot b+a$$, and factor to $$(10)a=(b+1)a$$. Dividing by $$a$$, we have that $$b+1=10$$. Therefore, the units digit, $$b$$, is $$9$$. 
A $$2-$$digit number is such that the product of the digits adding the sum of the digits is equal to the number itself. What is the ones digit of the number? 

(1) $$1$$ 
(2) $$3$$ 
(3) $$5$$ 
(4) $$7$$ 
(5) $$9$$ 