72 Is 90 Of What Number

72 is 90% of What Number? Solving Percentage Problems

This article will guide you through solving the percentage problem: "72 is 90% of what number?". We'll break down the process step-by-step, explain the underlying math, and provide you with a formula you can use for similar problems. This is a common type of percentage problem encountered in various fields like mathematics, finance, and everyday life. Understanding how to solve it is a valuable skill.

Understanding the Problem

The core of the problem lies in understanding the relationship between percentages, parts, and wholes. We know that 72 represents 90% of a larger, unknown number. Our goal is to find that unknown number. This involves working backward from the percentage to find the original whole.

Method 1: Using the Percentage Formula

The most straightforward approach is using the basic percentage formula:

• Part = Percentage × Whole

In our problem:

• Part = 72
• Percentage = 90% = 0.90 (Remember to convert the percentage to a decimal by dividing by 100)
• Whole = x (This is the unknown number we need to find)

Substituting these values into the formula, we get:

72 = 0.90x

To solve for x, we divide both sides of the equation by 0.90:

x = 72 / 0.90 = 80

Therefore, 72 is 90% of 80.

Method 2: Using Proportions

Another way to solve this is by setting up a proportion:

• 72/x = 90/100

This proportion states that the ratio of the part (72) to the whole (x) is equal to the ratio of the percentage (90) to 100%. To solve for x, we cross-multiply:

72 * 100 = 90 * x

7200 = 90x

x = 7200 / 90 = 80

Again, we find that x = 80.

Applying this to other Percentage Problems

The methods outlined above can be applied to any problem where you need to find the whole number given a part and its percentage. Simply substitute the known values into the formula or proportion and solve for the unknown. Remember to always convert percentages to decimals before using them in calculations.

Real-World Applications

Understanding percentage calculations is crucial in many real-world situations, including:

• Finance: Calculating discounts, interest rates, taxes, and profit margins.
• Statistics: Analyzing data and interpreting results.
• Everyday life: Figuring out tips, sales, and comparing prices.

Conclusion

Solving percentage problems like "72 is 90% of what number?" might seem daunting initially, but by understanding the underlying concepts and utilizing the appropriate methods, the solution becomes clear. Whether you use the percentage formula or proportions, both lead to the same answer: 80. Mastering these techniques equips you with a valuable skill applicable across diverse situations.