Math Problem Statement

A store has clearance items that have been marked down by 60%. They are having a sale, advertising an additional 25% off clearance items. What percent of the original price do you end up paying?

%

Give your answer accurate to at least one decimal place.

Solution

To solve this, we will calculate how much of the original price remains after the two discounts are applied consecutively.

  1. Step 1: Apply the first discount (60% off)
    After a 60% discount, you're paying 100%60%=40%100\% - 60\% = 40\% of the original price.

  2. Step 2: Apply the second discount (25% off the clearance price)
    Now, an additional 25% is taken off the remaining 40% of the original price. You're paying 100%25%=75%100\% - 25\% = 75\% of this clearance price.

  3. Step 3: Calculate the final percentage
    You pay 75% of 40% of the original price, which is: 0.75×0.40=0.300.75 \times 0.40 = 0.30 This means you end up paying 30% of the original price.

Thus, the final answer is 30% of the original price.

Would you like further details on this?


Here are 5 related questions for practice:

  1. If an item was originally $80, how much would you pay after these discounts?
  2. What would be the final price if the first discount was 50% and the second was 20% off the clearance price?
  3. How much would you save on an item priced at $120 with a 60% markdown and additional 25% off?
  4. If the sale had an additional 30% off instead of 25%, what would the final percentage paid be?
  5. What if the second discount was applied first, followed by the initial clearance discount—how would the result change?

Tip: Always apply consecutive percentage discounts on the reduced price from the previous step, not directly on the original price!

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Math Problem Analysis

Mathematical Concepts

Percentages
Sequential Discounts
Multiplication of Fractions

Formulas

Remaining Percentage = (1 - discount1) * (1 - discount2) * 100

Theorems

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Suitable Grade Level

Grades 6-8