Math Problem Statement

Calculate the percentage decrease based on the given original and new values.

Solution

The image you've uploaded contains a table with calculations related to percent decrease. It seems to be a comparison of original values with the decrease in value, followed by the calculation of the percentage decrease.

Here’s a breakdown of the table content:

Table Columns:

  1. Original Value
  2. New Value
  3. Decrease in Value
  4. Percentage Decrease
  5. Solution (not filled in the image)

Data:

  • Row 1:
    • Original Value: 100
    • New Value: 90
    • Decrease in Value: 10
    • Percentage Decrease: 10%
  • Row 2:
    • Original Value: 180
    • New Value: 120
    • Decrease in Value: 60
    • Percentage Decrease: 33.33%
  • Row 3:
    • Original Value: 1,200
    • New Value: 270
    • Decrease in Value: 930
    • Percentage Decrease: 77.5%
  • Row 4:
    • Original Value: 1,600
    • New Value: 400
    • Decrease in Value: 1,200
    • Percentage Decrease: 75%

Calculations Explained:

The formula for percentage decrease is:

Percentage Decrease=(Original ValueNew ValueOriginal Value)×100%\text{Percentage Decrease} = \left(\frac{\text{Original Value} - \text{New Value}}{\text{Original Value}}\right) \times 100\%

Using this formula:

  1. For the first row:

    • Decrease = 10090=10100 - 90 = 10
    • Percentage Decrease = 10100×100=10%\frac{10}{100} \times 100 = 10\%
  2. For the second row:

    • Decrease = 180120=60180 - 120 = 60
    • Percentage Decrease = 60180×10033.33%\frac{60}{180} \times 100 \approx 33.33\%
  3. For the third row:

    • Decrease = 1,200270=9301,200 - 270 = 930
    • Percentage Decrease = 9301200×10077.5%\frac{930}{1200} \times 100 \approx 77.5\%
  4. For the fourth row:

    • Decrease = 1,600400=1,2001,600 - 400 = 1,200
    • Percentage Decrease = 12001600×100=75%\frac{1200}{1600} \times 100 = 75\%

If you need any specific detail or want to discuss a particular part of this table, please let me know!

Questions:

  1. How would you calculate the percentage increase if the new value was higher than the original value?
  2. What would the percentage decrease be if the new value was zero?
  3. How do you interpret a 100% decrease in value?
  4. How can percentage decrease be useful in real-world applications?
  5. What is the significance of the "Solution" column in this table?

Tip:

Always double-check your percentage calculations to ensure accuracy, especially when dealing with large datasets or financial data.

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Math Problem Analysis

Mathematical Concepts

Percentage
Percentage Decrease
Arithmetic

Formulas

Percentage Decrease = ((Original Value - New Value) / Original Value) * 100

Theorems

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Suitable Grade Level

Grades 6-8