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%:

Discounted price after 25% discount=65.69×(10.25)=65.69×0.75=49.2675\text{Discounted price after 25\% discount} = 65.69 \times (1 - 0.25) = 65.69 \times 0.75 = 49.2675

Apply the second discount of 36%:

Final cost price after 36% discount=49.2675×(10.36)=49.2675×0.64=31.5312\text{Final cost price after 36\% discount} = 49.2675 \times (1 - 0.36) = 49.2675 \times 0.64 = 31.5312 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: Markup=Selling PriceCost Price=52.9631.53=21.43\text{Markup} = \text{Selling Price} - \text{Cost Price} = 52.96 - 31.53 = 21.43

Step 3: Calculate the markup as a percent of cost.

The markup percentage is given by: Markup Percent=(MarkupCost Price)×100=(21.4331.53)×10067.96%\text{Markup Percent} = \left(\frac{\text{Markup}}{\text{Cost Price}}\right) \times 100 = \left(\frac{21.43}{31.53}\right) \times 100 \approx 67.96\%

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:

  1. How does a successive discount differ from a single equivalent discount?
  2. How would the markup change if the selling price were increased to $55?
  3. What is the importance of markup in retail pricing strategy?
  4. How would the calculation change if the discounts were applied in reverse order?
  5. 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