Math Problem Statement
The net price of an item after trade discounts of 32.00%, 14.50%, and 5.50% is $3,600.00.
a. Calculate the regular selling price of the goods.
Round to the nearest cent
b. Calculate the equivalent discount rate of the series of discount rates.
%
Round to two decimal places
Solution
Let's solve each part of the problem step by step.
Part (a): Calculate the Regular Selling Price
Given the net price is $3,600 after three trade discounts of 32.00%, 14.50%, and 5.50%, we need to find the regular selling price.
Let the regular selling price be .
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Apply the first discount (32.00%):
The price after the first discount:
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Apply the second discount (14.50%):
The price after the second discount:
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Apply the third discount (5.50%):
The net price after all three discounts:
Solving for :
Let's calculate this:
So, the regular selling price of the goods is $6,558.86.
Part (b): Calculate the Equivalent Discount Rate
The equivalent discount rate is the single discount that would give the same net price as the series of discounts.
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The combined discount factor from all three discounts:
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The equivalent discount rate is:
Convert to percentage:
So, the equivalent discount rate is 45.12%.
Would you like further explanation or have additional questions?
Here are 8 related questions to consider:
- What would the net price be if only a single 32.00% discount was applied to the regular price?
- How does the net price change if the order of applying the discounts is reversed?
- How would the equivalent discount rate change if an additional 10% discount was applied after the 5.50% discount?
- What would the regular selling price be if the net price after the discounts was $4,000 instead of $3,600?
- What is the impact of increasing the first discount from 32.00% to 35.00% on the equivalent discount rate?
- How does a 5.50% discount compare to a 5.00% discount in terms of the final net price?
- What would be the net price if only the first two discounts (32.00% and 14.50%) were applied?
- How would the equivalent discount rate change if the regular price increased by 5%?
Tip: When dealing with multiple discounts, always apply each discount sequentially to get an accurate final price, and use the combined discount factor to find an equivalent single discount rate.
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Math Problem Analysis
Mathematical Concepts
Percentages
Discounts
Equivalence
Formulas
Discount calculation formula
Theorems
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Suitable Grade Level
High School
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