Understanding the Percentage Problem with Three Numbers

This problem involves comparing two numbers to a third number using percentages and then finding the relationship between the first two numbers as a percentage.

We are given that:

• The first number is 28% less than a third number.
• The second number is 25% less than the same third number.
• We need to find what percentage the first number is of the second number.

Setting up the Calculation for Number Comparison

Let's assume the third number is \(100\). This makes calculating percentages easier.

• Calculating the First Number:
  The first number is 28% less than the third number (\(100\)).
  Decrease = 28% of \(100 = \frac{28}{100} \times 100 = 28\).
  First Number = Third Number - Decrease = \(100 - 28 = 72\).
• Calculating the Second Number:
  The second number is 25% less than the third number (\(100\)).
  Decrease = 25% of \(100 = \frac{25}{100} \times 100 = 25\).
  Second Number = Third Number - Decrease = \(100 - 25 = 75\).

Now we have:

Calculating What Percent the First Number is of the Second

The question asks: "What percent is the first number of the second number?"

This can be written as the formula:

$$ \text{Percentage} = \left( \frac{\text{First Number}}{\text{Second Number}} \right) \times 100\% $$

Substitute the values we found:

$$ \text{Percentage} = \left( \frac{72}{75} \right) \times 100\% $$

Step-by-Step Solution

Now, let's simplify the fraction and perform the calculation:

1. We have the ratio \( \frac{72}{75} \).
2. Both 72 and 75 are divisible by 3.
   \( 72 \div 3 = 24 \)
   \( 75 \div 3 = 25 \)
   So, the fraction simplifies to \( \frac{24}{25} \).
3. Now, multiply the simplified fraction by 100% to get the percentage:
   \( \frac{24}{25} \times 100\% \)
4. Calculate \( \frac{100}{25} = 4 \).
5. Multiply the result by 24:
   \( 24 \times 4\% = 96\% \)

So, the first number is 96% of the second number.

Conclusion

By first determining the values of the first and second numbers relative to a chosen third number (like 100) and then calculating the ratio of the first number to the second number as a percentage, we find the required value.

Revision Table: Key Concepts Reviewed

Additional Information: Percentage Applications

Percentage is a fundamental concept used widely in various fields including finance, statistics, and everyday calculations. Understanding how to calculate percentage increase, decrease, and percentage of a quantity is crucial for solving many quantitative problems.

• Finding "X% of Y" means \( \frac{X}{100} \times Y \).
• Finding "What percent is X of Y" means \( \left( \frac{X}{Y} \right) \times 100\% \).
• "X% less than Y" means \( Y - \left( \frac{X}{100} \times Y \right) \) or \( Y \left( 1 - \frac{X}{100} \right) \).