Math Problem Statement
A sports store purchased tennis racquets for $65.6965.69 less 2525% for purchasing more than 100 items, and a further 36 %36% was reduced for purchasing the racquets in October. The racquets were sold to customers for $ 52.96. What is the markup as a percent of cost?
Solution
Let's calculate the markup percentage step-by-step based on the given information.
Step 1: Calculate the cost price of the tennis racquets.
The initial cost per racquet is $65.69. The store received two successive discounts:
- A 25% discount for purchasing more than 100 items.
- A 36% discount for purchasing in October.
Apply the first discount of 25%:
Apply the second discount of 36%:
Thus, the final cost per racquet is $31.53.
Step 2: Calculate the markup.
The selling price of the racquet is $52.96, and the cost price is $31.53. The markup is calculated as:
Step 3: Calculate the markup as a percent of cost.
The markup percentage is given by:
Final Answer:
The markup as a percent of cost is approximately 67.96%.
Would you like further details or have any questions about the steps?
Here are 5 related questions to expand your understanding:
- How does a successive discount differ from a single equivalent discount?
- How would the markup change if the selling price were increased to $55?
- What is the importance of markup in retail pricing strategy?
- How would the calculation change if the discounts were applied in reverse order?
- How is markup different from profit margin in percentage terms?
Tip: When multiple discounts are applied successively, always apply one at a time and multiply the price by the remaining percentage after each discount.
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Math Problem Analysis
Mathematical Concepts
Percentage Calculations
Successive Discounts
Markup Calculation
Formulas
Discounted Price = Original Price × (1 - Discount)
Markup = Selling Price - Cost Price
Markup Percentage = (Markup / Cost Price) × 100
Theorems
Percentage Theorem
Suitable Grade Level
Grades 8-10
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