2014 AMC 10B Problem 6

1. Pick an easy unit. Say one balloon normally costs $\$1$. Orvin can buy exactly $30$ balloons, so he has $\$30$.
2. Price of a sale pair. The first balloon costs $\$1$. The second is $\frac13$ off, so it costs $1 - \frac13 = \frac23$ of a dollar. One pair costs
$$1 + \frac23 = \frac53 \text{ dollars}.$$
3. How many pairs? Three pairs cost $3 \times \frac53 = \$5$. So every $\$5$ buys $3$ pairs, which is $6$ balloons.
4. Orvin has $\$30 = 6 \times \$5$, so he buys $6 \times 3 = 18$ pairs with nothing left over.
5. That is $18 \times 2 = 36$ balloons.

The answer is $\boxed{\textbf{(C)}\ 36}$.

Using the regular price as the unit turns the budget into a plain number ($30$). A "buy one, get one at a discount" deal repeats in pairs, so work out the cost of one pair and see how many pairs fit. It is also worth checking whether money is left over, since a leftover single balloon would cost full price; here the money runs out exactly.