John paid \( \$ 270 \) for a new mountain bicycle to sell in his shop. He wants to price it so that he can offer a \( 10 \% \) discount but still make \( 20 \% \) of the price he paid for it. At what price should the bike be marked? The bike should be marked for \( \$ 360 \). (Round to the nearest dollar as needed.)

To ensure John makes a \( 20\% \) profit after offering a \( 10\% \) discount, first, we calculate the desired selling price. He paid \( \$ 270 \), and a \( 20\% \) profit on that is \( 0.20 \times 270 = \$ 54 \). Adding that to the cost gives \( 270 + 54 = \$ 324 \). Next, to find the marked price, we need to account for the \( 10\% \) discount. If \( P \) is the marked price, then after a \( 10\% \) discount, he would charge \( 0.90P \). We set the equation \( 0.90P = 324 \), solving for \( P \) gives us \( P = \dfrac{324}{0.90} = \$ 360 \). So, to be able to discount the bike but still maintain his profit, John should mark it at **$360**.