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Chapter 11: Problem 1

The original selling price of an item at a store is 40 percent more than the cost of the item to the retailer. If the retailer reduces the price of the item by 15 percent of the original selling price, then the difference between the reduced price and the cost of the item to the retailer is what percent of the cost of the item to the retailer?

Short Answer

Expert verified
The difference between the reduced price and the cost to the retailer is 19% of the cost of the item to the retailer.

Step by step solution

01

Calculation of the Original Selling Price

Let's denote the original cost to the retailer with \( C \). Therefore, the original selling price (\( P \)) which is 40% more, would be: \( P = C + C \times 0.4 = 1.4C \)
02

Calculation of the Reduced Price

The price was then reduced by 15% of the original selling price, so the new reduced price (\( R \)) would be: \( R = P - P \times 0.15 = 1.4C - 0.15 \times 1.4C = 1.4C \times 0.85 \)
03

Calculation of the Difference (Reduced Price - Cost)

To find the difference (\( D \)) between the reduced price and the cost of the item to the retailer, subtract the cost from the reduced price: \( D = R - C = 1.4C \times 0.85 - C \)
04

Calculation of the Difference as Percentage of Cost

The last part of the problem requires us to find this difference as a percentage of the cost to the retailer. We solve for \( D \) as a percentage of the cost, i.e., \( \frac{D}{C} \times 100\% \). After plugging in the formula for \( D \) found in the previous step and simplifying, we find the answer

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