Math Problem Statement

A store buys a watch for $75 and marks it up by 40%. During a clearance sale, the price of the watch is reduced by 25%.

What is the final sale price of the watch? A.$70.50 B.$75.00 C.$72.50 D.$78.75

Solution

To find the final sale price of the watch, let's work through the problem step by step:

  1. Initial Cost: The store buys the watch for $75.

  2. Markup by 40%: The store marks up the price by 40%.

    • The markup is calculated as: 40% of 75=40100×75=0.40×75=3040\% \text{ of } 75 = \frac{40}{100} \times 75 = 0.40 \times 75 = 30
    • Therefore, the new price after markup is: 75+30=10575 + 30 = 105
  3. Clearance Sale Discount of 25%: During the clearance sale, the price is reduced by 25%.

    • The discount is calculated as: 25% of 105=25100×105=0.25×105=26.2525\% \text{ of } 105 = \frac{25}{100} \times 105 = 0.25 \times 105 = 26.25
    • Therefore, the final sale price is: 10526.25=78.75105 - 26.25 = 78.75

Thus, the final sale price of the watch is $78.75.

Answer: D. $78.75

Would you like more details on this or have any questions?

Here are 5 follow-up questions you might explore:

  1. What if the markup percentage were 50% instead of 40%?
  2. How would the final price change if the clearance discount were 30%?
  3. How can the final price be calculated using only percentages in one step?
  4. What would the store's profit be after selling the watch at the clearance price?
  5. How does the order of applying percentages (markup vs. discount) affect the final price?

Tip: When dealing with percentages, always apply them sequentially, unless you are given a combined percentage formula!

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Math Problem Analysis

Mathematical Concepts

Percentage Markup
Percentage Discount
Sequential Percentage Calculations

Formulas

Final price after markup = Original price + (Markup percentage × Original price)
Final price after discount = Marked price - (Discount percentage × Marked price)

Theorems

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Suitable Grade Level

Grades 6-8