Math Problem Statement

The price of an item has dropped to $81 today. Yesterday it was $180. Find the percentage decrease.

Solution

To find the percentage decrease, you can use the following formula:

Percentage Decrease=Old PriceNew PriceOld Price×100\text{Percentage Decrease} = \frac{\text{Old Price} - \text{New Price}}{\text{Old Price}} \times 100

In this case:

  • Old Price (Yesterday) = $180
  • New Price (Today) = $81

Let's plug these values into the formula:

Percentage Decrease=18081180×100=99180×10055%\text{Percentage Decrease} = \frac{180 - 81}{180} \times 100 = \frac{99}{180} \times 100 \approx 55\%

So, the percentage decrease is 55%.

Would you like more details or have any questions about the calculation?

Here are some related questions for further exploration:

  1. How would you calculate a percentage increase if the price had risen?
  2. What is the formula for percentage change in general (whether increase or decrease)?
  3. If the price dropped to $100 instead, what would the percentage decrease be?
  4. Can you explain how to find the original price if you know the final price and the percentage decrease?
  5. How would you apply this formula in other real-world situations like discounts or interest rates?

Tip: When calculating percentage changes, always compare the difference relative to the original value.

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Math Problem Analysis

Mathematical Concepts

Percentage Decrease
Basic Arithmetic

Formulas

Percentage Decrease = ((Old Price - New Price) / Old Price) * 100

Theorems

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Suitable Grade Level

Grades 6-8