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Royal Furniture bought a sofa for [tex]\$800[/tex]. The sofa had a [tex]\$1,400[/tex] list price. What was the trade discount rate Royal received? Round to the nearest hundredth percent.

Answer :

To determine the trade discount rate Royal Furniture received on the sofa, we can follow these steps:

1. Identify the List Price and Purchase Price:
- The list price (original price) of the sofa is [tex]$1,400.
- The purchase price (price paid) of the sofa is $[/tex]800.

2. Calculate the Trade Discount:
The trade discount is the difference between the list price and the purchase price.
[tex]\[
\text{Trade Discount} = \text{List Price} - \text{Purchase Price} = 1400 - 800 = 600
\][/tex]
So, the trade discount is $600.

3. Determine the Trade Discount Rate:
The trade discount rate is calculated by dividing the trade discount by the list price and then converting it into a percentage.
[tex]\[
\text{Trade Discount Rate} = \left( \frac{\text{Trade Discount}}{\text{List Price}} \right) \times 100 = \left( \frac{600}{1400} \right) \times 100
\][/tex]
[tex]\[
\approx 42.86\%
\][/tex]

4. Round to the Nearest Hundredth Percent:
The calculated trade discount rate is approximately 42.857142857142854%, and when rounded to the nearest hundredth percent (two decimal places), it is 42.86%.

Therefore, the trade discount rate that Royal Furniture received is approximately 42.86%.

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