find a and b in $a67.9b In the following problem, $A$ and $B$ are single digits. 

A store sold 72 decks of cards for $\$A67.9B$. Find $A + B$.

Here is as far as I can go: The price of each deck of card should be $\frac{A67.9B}{72}$, and $72=2^3\times 3^2$. How do I find $A$ and $B$ from here?

Dealing with the number in cents, we know that since it's divisible by 72,  it's also divisible by 9. This means that the sum of its digits must be a multiple of 9. (see Casting out 9s)
The sum of the digits is $(A+B+6+7+9) mod 9 = 0$
So we have, simplifying, $(A+B+4) mod 9 = 0$;
The only sum of digits $A+B$ that meets this specification is $A+B = 5$
