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Chapter 10: Problem 5

During a sale, a store decreases the prices on all of its scarves by 25 to 50 percent. If all of the scarves in the store were originally priced at \(\$ 20,\) which of the following prices could be the sale price of a scarf? Indicate all such prices. A. $$\$ 8$$ B. $$\$ 10$$ C. $$\$ 12$$ D. $$\$ 14$$ E. $$\$ 16$$

Short Answer

Expert verified
The possible prices for a scarf on sale are \$10 and \$12, so the correct answers are options B and C.

Step by step solution

01

Identify the Original Price

The original price of each scarf is \$20.
02

Compute the Prices After the Maximum and Minimum Discounts

First, calculate the price after a 25 percent discount, and then after a 50 percent discount. A 25 percent discount on \$20 is \$5 (\(0.25 \times 20\)), so the price of the scarf after this discount is \$15, i.e., \(20 - 5\). A 50 percent discount on \$20 is \$10 (\(0.50 \times 20\)), so the price of the scarf after this discount is just \$10, i.e., \(20 - 10\).
03

Compare Given Prices With Range

Now compare the prices given in the options with the price range calculated in step 2. Prices that are within the range from \$10 to \$15, inclusive, are the possible sale prices of a scarf.

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