What Percent Of 75 Is 90

What Percent of 75 is 90? Understanding Percentage Calculations and Their Applications

The question, "What percent of 75 is 90?" might seem simple at first glance. However, understanding how to solve this type of problem unlocks a world of practical applications in various fields, from calculating discounts and taxes to understanding statistical data and financial reports. This comprehensive guide will not only answer the question but will also delve into the underlying mathematical concepts and explore numerous real-world examples.

Understanding Percentages

A percentage is a way of expressing a number as a fraction of 100. The word "percent" literally means "per hundred" – it represents a portion out of a whole, where the whole is considered to be 100 units. For example, 50% means 50 out of 100, which is equivalent to ½ or 0.5.

Solving "What Percent of 75 is 90?"

To find out what percent of 75 is 90, we need to set up a simple equation. Let's represent the unknown percentage as 'x'. Our equation will look like this:

x% of 75 = 90

We can rewrite this equation as:

(x/100) * 75 = 90

Now, let's solve for 'x':

1. Multiply both sides by 100: 75x = 9000
2. Divide both sides by 75: x = 9000 / 75
3. Calculate the result: x = 120

Therefore, 90 is 120% of 75.

This result might seem counterintuitive at first – how can a part be larger than the whole? This is perfectly possible when dealing with percentages. It simply means that 90 is more than 75; it represents an increase or growth relative to 75 as the base value.

Different Approaches to Solving Percentage Problems

While the equation method is straightforward, there are other ways to approach percentage problems, depending on your preference and the complexity of the problem. Let's explore a few alternative methods:

1. Using Proportions:

Proportions provide a visual and intuitive way to solve percentage problems. We can set up a proportion like this:

x/100 = 90/75

Cross-multiplying, we get:

75x = 9000

Solving for x, we arrive at the same answer: x = 120%

2. Using Decimal Equivalents:

Percentages can easily be converted to decimals by dividing by 100. For instance, 120% is equal to 1.20. We can use this conversion to solve the problem as follows:

1.20 * 75 = 90

This confirms our previous answer.

Real-World Applications of Percentage Calculations

Percentage calculations are ubiquitous in daily life. Here are some examples:

1. Business and Finance:

• Profit margins: Businesses calculate profit margins as a percentage of revenue to assess their profitability.
• Interest rates: Banks and other financial institutions use percentage interest rates to determine loan repayments and savings account growth.
• Discounts and sales tax: Retailers use percentages to express discounts and sales tax on products. Calculating a 20% discount on a $100 item involves finding 20% of $100, which is $20. The final price would be $80.
• Investment returns: Investors use percentages to track the performance of their investments, comparing the gains or losses relative to the initial investment amount.

2. Science and Statistics:

• Data analysis: Scientists and statisticians frequently use percentages to represent data in graphs, charts, and reports. Percentages are essential for presenting relative frequencies and probabilities.
• Population growth: Population growth is often expressed as a percentage increase over a given period.
• Experimental results: In experiments, percentages are used to express the success rate or effectiveness of treatments or interventions. For example, a vaccine's efficacy might be expressed as a percentage reduction in the incidence of a disease.

3. Everyday Life:

• Tip calculations: Calculating a tip in a restaurant often involves finding a percentage (e.g., 15% or 20%) of the total bill.
• Grade calculations: Academic grades are sometimes expressed as percentages to reflect the proportion of correct answers or the overall performance in a course.
• Household budgets: Managing household finances often involves using percentages to allocate funds to different categories like housing, food, transportation, etc.

Expanding on Percentage Concepts: Percentage Increase and Decrease

The problem "What percent of 75 is 90?" implicitly involves a percentage increase. Let's examine how to calculate percentage increases and decreases:

Percentage Increase: This refers to the increase in a value expressed as a percentage of the original value. The formula is:

Percentage Increase = [(New Value - Original Value) / Original Value] * 100

In our example, the percentage increase from 75 to 90 is:

[(90 - 75) / 75] * 100 = 20%

This tells us that 90 is 20% more than 75.

Percentage Decrease: This refers to the decrease in a value expressed as a percentage of the original value. The formula is:

Percentage Decrease = [(Original Value - New Value) / Original Value] * 100

For instance, if a value decreases from 100 to 80, the percentage decrease is:

[(100 - 80) / 100] * 100 = 20%

This means the value decreased by 20% of its original amount.

Advanced Percentage Applications: Compound Interest

Compound interest is a powerful concept where interest earned is added to the principal amount, and subsequent interest calculations are based on the increased principal. It is frequently used in finance, and understanding percentages is crucial for grasping this concept.

The formula for compound interest is:

A = P (1 + r/n)^(nt)

Where:

• A = the future value of the investment/loan, including interest
• P = the principal investment amount (the initial deposit or loan amount)
• r = the annual interest rate (decimal)
• n = the number of times that interest is compounded per year
• t = the number of years the money is invested or borrowed for

Compound interest calculations rely heavily on percentages to determine the growth of an investment or the accumulation of debt over time.

Conclusion

The question, "What percent of 75 is 90?" serves as a gateway to understanding the broad applicability of percentage calculations. From simple everyday tasks to complex financial models, percentages are essential for expressing proportions, analyzing data, and making informed decisions. Mastering percentage calculations equips you with a crucial skill for navigating various aspects of life, both personal and professional. By understanding the underlying concepts and the various approaches to solving percentage problems, you can confidently tackle numerous challenges that involve this fundamental mathematical concept.