Understanding the Percentage Problem

The question asks us to find a certain percentage (89%) of a number, given what another percentage (21%) of that same number is. This type of problem requires us to first determine the original number before calculating the desired percentage.

We are given that 21% of a number is 546. Let the unknown number be represented by ${N}$. We can write this information as a mathematical equation:

$\text{21\% of } N = 546$

In mathematical terms, percentage means 'out of 100'. So, 21% can be written as $\frac{21}{100}$ or 0.21.

The equation becomes:

$0.21 \times N = 546$

Finding the Original Number

To find the original number ${N}$, we need to isolate ${N}$ in the equation. We can do this by dividing both sides of the equation by 0.21:

$N = \frac{546}{0.21}$

Performing the division:

$N = 2600$

So, the original number is 2600.

Calculating 89% of the Number

Now that we know the original number is 2600, we can find 89% of this number. We need to calculate:

$\text{89\% of 2600}$

Similarly, 89% can be written as $\frac{89}{100}$ or 0.89.

The calculation is:

$0.89 \times 2600$

Multiplying these values:

$0.89 \times 2600 = 2314$

Therefore, 89% of the number is 2314.

Step-by-Step Solution Summary

1. Identify the given information: 21% of a number is 546.
2. Set up an equation to represent the given information: $0.21 \times N = 546$.
3. Solve for the unknown number ${N}$ by dividing 546 by 0.21: $N = \frac{546}{0.21} = 2600$. The original number is 2600.
4. Identify what needs to be found: 89% of the number.
5. Calculate 89% of the original number (2600): $0.89 \times 2600 = 2314$.

The result is 2314.

Verification

We can quickly check if our original number calculation is correct:

What is 21% of 2600?

$0.21 \times 2600 = 546$

This matches the information given in the question, confirming that 2600 is indeed the correct original number.

Final Answer

Based on our calculations, 89% of the number is 2314.

Revision Table: Percentage Calculation

Additional Information: Percentage Concepts

Percentages are a fundamental concept in mathematics used to represent a part of a whole as a fraction of 100. They are widely used in various fields, including finance, statistics, and everyday calculations like discounts and taxes.

• Converting Percentage to Decimal: Divide the percentage by 100. For example, ${21\% = 21/100 = 0.21}$.
• Converting Decimal to Percentage: Multiply the decimal by 100. For example, ${0.89 = 0.89 \times 100 = 89\%}$.
• Finding 'what percentage' one number is of another: Divide the first number by the second number and multiply by 100. For example, to find what percentage 50 is of 200, calculate $\frac{50}{200} \times 100\% = 0.25 \times 100\% = 25\%$.