90 Is 75 Of What Number

90 is 75% of What Number? Solving Percentage Problems

This article will guide you through solving the percentage problem: "90 is 75% of what number?". We'll break down the solution step-by-step, explore different methods, and offer tips for tackling similar percentage questions. Understanding percentage calculations is crucial in various aspects of life, from calculating discounts and tax to understanding financial data and statistics. This seemingly simple problem provides a great opportunity to master the underlying concepts.

Understanding the Problem

The question "90 is 75% of what number?" asks us to find the original number (often represented by 'x') from which 75% equals 90. We can represent this problem algebraically as:

0.75 * x = 90

Method 1: Algebraic Approach

This is the most direct and commonly used method. We solve the equation for 'x':

1. Convert the percentage to a decimal: 75% = 0.75
2. Set up the equation: 0.75x = 90
3. Isolate 'x': Divide both sides of the equation by 0.75: x = 90 / 0.75
4. Calculate: x = 120

Therefore, 90 is 75% of 120.

Method 2: Using Proportions

This method uses the concept of ratios and proportions to solve the problem. We can set up a proportion:

75/100 = 90/x

This reads as "75 is to 100 as 90 is to x". Cross-multiply to solve:

75x = 9000

x = 9000 / 75

x = 120

Again, we find that 90 is 75% of 120.

Method 3: The Percentage Formula

The basic percentage formula can be rearranged to solve this type of problem. The formula is:

(Part / Whole) * 100 = Percentage

We know the part (90) and the percentage (75%). We need to find the whole (x). Rearranging the formula:

Whole = (Part / Percentage) * 100

Substituting the known values:

x = (90 / 75) * 100

x = 120

This method, like the others, confirms that 90 is 75% of 120.

Tips for Solving Percentage Problems

• Understand the terms: Clearly identify the 'part', 'whole', and 'percentage' in the problem.
• Convert percentages to decimals: This simplifies calculations.
• Use a calculator: For more complex problems, a calculator is helpful for accuracy.
• Check your work: Always verify your answer by plugging it back into the original problem.

Mastering percentage calculations is essential for various applications, from everyday budgeting and shopping to more complex financial analysis and scientific calculations. By understanding the different methods outlined above, you can confidently tackle a wide range of percentage problems. Remember to practice regularly to solidify your understanding and improve your problem-solving skills.