36 Is 15 Of What Number

36 is 15% of What Number? Solving Percentage Problems

This article will guide you through solving the percentage problem: "36 is 15% of what number?". We'll break down the process step-by-step, explaining the underlying concepts and providing a formula you can use to solve similar problems. Understanding percentages is crucial in various aspects of life, from calculating discounts and taxes to analyzing data and understanding financial reports. This simple example demonstrates a fundamental skill applicable to many scenarios.

Understanding the Problem

The question "36 is 15% of what number?" is asking us to find the whole number (or the base) when we know a part of it (36) and the percentage that part represents (15%). This type of problem involves working backward from a percentage to find the original value.

Method 1: Using the Percentage Formula

The standard percentage formula is:

(Part / Whole) * 100 = Percentage

In our problem:

• Part = 36
• Percentage = 15%
• Whole = x (this is what we need to find)

Substituting these values into the formula, we get:

(36 / x) * 100 = 15

Now, we solve for 'x':

1. Divide both sides by 100: 36 / x = 0.15
2. Multiply both sides by x: 36 = 0.15x
3. Divide both sides by 0.15: x = 36 / 0.15
4. Calculate: x = 240

Therefore, 36 is 15% of 240.

Method 2: Using Proportions

We can also solve this using proportions. We can set up a proportion where we equate the ratio of the part to the whole with the ratio of the percentage to 100:

36/x = 15/100

Cross-multiply:

36 * 100 = 15 * x

3600 = 15x

Divide both sides by 15:

x = 3600 / 15

x = 240

Again, we find that 36 is 15% of 240.

Practical Applications

Understanding how to solve percentage problems like this is valuable in many real-world situations, such as:

• Sales and discounts: Calculating the original price of an item after a discount.
• Finance: Determining interest rates and loan repayments.
• Data analysis: Interpreting percentages in graphs and charts.
• Statistics: Understanding proportions and probabilities.

Conclusion

Solving the problem "36 is 15% of what number?" demonstrates a fundamental skill in working with percentages. Both the formula method and the proportions method provide effective ways to arrive at the correct answer: 240. By mastering these methods, you’ll be well-equipped to handle various percentage calculations encountered in daily life and professional settings. Remember to practice these methods to solidify your understanding and improve your speed and accuracy.