A local store is running a buy one, get 30% off sale for one of its clothing products. If you buy two shirts, the store charges a regular price $r$ dollars for the first shirt and gives you a 30% discount on the second shirt. The sales tax on orders is 12%. Which of the following expressions gives the total, in dollars, one would expect to pay if someone were to buy two shirts during the sale?

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A $30\%$ discount is equivalent to taking $70\%$ of a number. The discounted shirt should cost:

$$0.70r$$

We obtain this using the percent change equation, where the final value is equal to some initial value multiplied by the percent change:

$$\text{Final} = \text{Initial} \cdot (1\pm \text{percent change})$$ $$\text{Discounted price} = \text{Original price} \cdot (1 - \text{discount})$$ $$\text{Discounted price} = r \cdot (1-0.30)$$ $$\text{Discounted price} = 0.70r$$

Therefore, the cost of the original shirt and the discounted shirt is:

$$r + 0.70r$$

We can use the percent change equation again to calculate the cost after we apply the sales tax.

$$\text{Final} = \text{Initial} \cdot (1\pm \text{percent change})$$ $$\text{Price after tax} = \text{Price before tax} \cdot (1 + \text{tax})$$ $$\text{Price after tax} = (r + 0.70r) \cdot (1+0.12)$$ $$= \boxed{1.12(r+0.70r)}$$