Question

Debi purchased $108 worth of sheets at a sale on Labor Day weekend, when $1.50 was marked off every article. She returned the sheets on Thursday (she really didn't need sheets anyway), when everything was marked at regular prices. Because Judy is a good customer, the sales clerk gave her credit using regular prices and not sale prices, so Debi got more than $91 worth of credit. She was ecstatic about this, so she immediately exchanged the sheets for towels and washcloths. In exchange for one sheet, she was able to get a towel and a washcloth. (The towels, washcloths, and sheets were now all marked at regular prices.) She came home with 16 more articles than she'd had before. Because washcloths cost only $2.70, she took six more washcloths than towels. How many washcloths and towels did she buy, and how much would they have cost if Debi had bought them on Saturday at sale prices?

Answer 1

To solve this problem, we need to find the original price of the sheets and then use that information to calculate the number of washcloths and towels Debi purchased. The problem provides us with the sale price of the sheets, the amount of credit Debi received, and the cost of washcloths.

Step-by-step explanation:

To solve this problem, we can start by figuring out how much Debi paid for the sheets. Since $1.50 was marked off every article, the original price of each sheet was $1.50 higher than the sale price. Let's say the sale price of one sheet is x dollars. The original price would then be x + 1.50 dollars.

So, Debi purchased 108 / (x + 1.50) sheets on Labor Day weekend. She returned these sheets and received more than $91 worth of credit at regular prices.

Next, let's determine the number of washcloths and towels Debi bought. If Debi exchanged one sheet for a towel and a washcloth, it means she obtained 16 more articles in total. We know that she took six more washcloths than towels, and each washcloth costs $2.70.

Using this information, we can set up two equations:

washcloths = towels + 6

washcloths x 2.70 + towels x price_of_towel = 16

This system of equations can then be solved to determine the number of washcloths and towels Debi bought, as well as the price of a towel.