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Problem-Solving and Data Analysis / Percentages Difficulty: Hard

A reseller buys certain books for a purchase price of $5.00$ dollars each and then marks them each for sale at a consumer price that is $270 percent sign$ of the purchase price. After $4$ months, any remaining books not yet sold are marked at a discounted price that is $70 percent sign$ off the consumer price. What is the discounted price of each of the remaining books, in dollars?

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Explanation

The correct answer is $4.05$ . It's given that the purchase price for certain books is $5.00$ dollars each. It's also given that each book is marked for sale at a consumer price that is $270 percent sign$ of the purchase price. Since the consumer price is $270 percent sign$ of the purchase price of $5.00$ dollars, it follows that the consumer price is $left parenthesis 2.7 right parenthesis left parenthesis 5.00 right parenthesis$ , or $13.50$ , dollars. It's given that after $4$ months, any remaining books are discounted at $70 percent sign$ off the consumer price. Thus, the discount amount is $left parenthesis 0.7 right parenthesis left parenthesis 13.50 right parenthesis$ , or $9.45$ , dollars. Subtracting the discount amount from the consumer price gives the discounted price of each of the remaining books: $13.50 - 9.45 = 4.05$ . Note that 4.05 and 81/20 are examples of ways to enter a correct answer.