Pre-Algebra · Superchallenge problem

A shopper buying a coat with a price of $\$P$ may use either a coupon for $15\%$ off or a coupon for $\$12$ off, but not both. An $8\%$ sales tax is then charged on the discounted price. Using the percent coupon makes the final bill, tax included, exactly $\$3.24$ smaller than using the dollar coupon. Find $P$.