59 Is 10% Of What Number A Step-by-Step Guide
Have you ever encountered a problem where you know a percentage of a number but need to find the whole number? These types of percentage problems are common in everyday life, from calculating discounts to understanding financial data. In this comprehensive guide, we will delve into the question, "59 is 10% of what number?" and equip you with the knowledge and skills to solve similar problems with confidence.
Understanding Percentages: The Foundation of Our Solution
Before we tackle the specific question, it's essential to grasp the fundamental concept of percentages. A percentage is simply a way of expressing a number as a fraction of 100. The word "percent" comes from the Latin "per centum," meaning "out of one hundred." Therefore, 10% means 10 out of every 100, or 10/100. This can also be expressed as the decimal 0.10.
Percentages are incredibly versatile and are used in various contexts, such as:
- Discounts: When a store offers a 20% discount, it means you'll pay 20% less than the original price.
- Interest rates: Interest rates on loans and savings accounts are expressed as percentages.
- Statistics: Percentages are used to represent proportions and distributions in data sets.
- Taxes: Sales tax and income tax are calculated as percentages of the purchase price or income.
To work with percentages effectively, it's crucial to understand how to convert them to decimals and fractions, and vice versa. This will allow us to perform calculations and solve percentage-related problems.
Converting Percentages to Decimals
To convert a percentage to a decimal, you simply divide the percentage by 100. For example:
- 10% = 10 / 100 = 0.10
- 25% = 25 / 100 = 0.25
- 75% = 75 / 100 = 0.75
- 120% = 120 / 100 = 1.20
Converting Percentages to Fractions
To convert a percentage to a fraction, you write the percentage as a fraction with a denominator of 100. Then, simplify the fraction if possible. For example:
- 10% = 10 / 100 = 1 / 10
- 25% = 25 / 100 = 1 / 4
- 75% = 75 / 100 = 3 / 4
Converting Decimals to Percentages
To convert a decimal to a percentage, you multiply the decimal by 100. For example:
- 0.10 = 0.10 * 100 = 10%
- 0.25 = 0.25 * 100 = 25%
- 0.75 = 0.75 * 100 = 75%
Converting Fractions to Percentages
To convert a fraction to a percentage, you first convert the fraction to a decimal by dividing the numerator by the denominator. Then, multiply the decimal by 100. For example:
- 1 / 10 = 0.10 = 0.10 * 100 = 10%
- 1 / 4 = 0.25 = 0.25 * 100 = 25%
- 3 / 4 = 0.75 = 0.75 * 100 = 75%
With a solid understanding of percentages and how to convert them between different forms, we are now well-equipped to tackle our problem.
Solving the Problem: "59 is 10% of What Number?"
Now, let's address the question at hand: "59 is 10% of what number?" To solve this, we can use the following steps:
Step 1: Translate the Problem into an Equation
The first step is to translate the word problem into a mathematical equation. We can represent the unknown number with the variable "x." The problem states that 59 is 10% of x. We can write this as:
59 = 10% of x
Since "of" in mathematics often means multiplication, we can rewrite the equation as:
59 = 10% * x
Step 2: Convert the Percentage to a Decimal
To perform calculations with percentages, we need to convert them to decimals. As we learned earlier, we can convert 10% to a decimal by dividing by 100:
10% = 10 / 100 = 0.10
Now, we can substitute this value back into our equation:
59 = 0.10 * x
Step 3: Isolate the Variable (x)
Our goal is to find the value of x. To do this, we need to isolate x on one side of the equation. Since x is being multiplied by 0.10, we can isolate x by dividing both sides of the equation by 0.10:
59 / 0.10 = (0.10 * x) / 0.10
This simplifies to:
x = 59 / 0.10
Step 4: Perform the Calculation
Now, we simply need to perform the division to find the value of x:
x = 59 / 0.10 = 590
Therefore, 59 is 10% of 590.
Verifying the Solution: Ensuring Accuracy
It's always a good practice to verify your solution to ensure accuracy. To do this, we can calculate 10% of 590 and see if it equals 59.
10% of 590 = 0.10 * 590 = 59
Since our calculation confirms that 10% of 590 is indeed 59, we can be confident that our solution is correct.
Alternative Method: Using Proportions
Another way to solve percentage problems is by using proportions. A proportion is an equation that states that two ratios are equal. In this case, we can set up a proportion to represent the relationship between 59, 10%, and the unknown number.
Step 1: Set up the Proportion
We can set up the following proportion:
59 / x = 10 / 100
This proportion states that the ratio of 59 to the unknown number (x) is equal to the ratio of 10 to 100.
Step 2: Cross-Multiply
To solve the proportion, we can cross-multiply. This means multiplying the numerator of the first fraction by the denominator of the second fraction, and vice versa:
59 * 100 = 10 * x
This simplifies to:
5900 = 10x
Step 3: Isolate the Variable (x)
To isolate x, we can divide both sides of the equation by 10:
5900 / 10 = (10x) / 10
This simplifies to:
x = 590
As you can see, using proportions yields the same result as our previous method. This demonstrates that there can be multiple approaches to solving percentage problems.
Real-World Applications: Where This Knowledge Comes in Handy
Understanding how to solve percentage problems like "59 is 10% of what number?" is not just an academic exercise. This knowledge has practical applications in various real-world scenarios. Let's explore a few examples:
1. Financial Planning
When dealing with finances, percentages are ubiquitous. Imagine you want to save a certain amount of money for a down payment on a house. You might set a goal to save 10% of your monthly income. If you know how much you want to save (e.g., $590) and that this represents 10% of your income, you can calculate your required monthly income using the same method we used earlier. This helps you create a realistic budget and track your progress towards your financial goals.
2. Retail and Discounts
As consumers, we often encounter discounts expressed as percentages. Suppose a store is offering a 20% discount on an item you want to purchase. If the discounted price is $59, you can use your knowledge of percentages to calculate the original price of the item. This allows you to assess whether the discount is truly a good deal and make informed purchasing decisions.
3. Sales and Commissions
In sales roles, commissions are often calculated as a percentage of sales revenue. If a salesperson earns a 10% commission and receives a commission check for $59, they can determine their total sales revenue for that period. This helps them track their performance and understand their earnings potential.
4. Data Analysis and Statistics
Percentages are widely used in data analysis and statistics to represent proportions and distributions. For example, a survey might reveal that 10% of respondents prefer a certain product. If the survey included 59 respondents who prefer the product, you can calculate the total number of survey participants. This type of analysis is essential for market research, public opinion polling, and various other fields.
5. Weight Loss and Fitness
Percentages can also be helpful in tracking progress towards weight loss or fitness goals. If you've lost 59 pounds, and this represents 10% of your starting weight, you can calculate your initial weight. This provides a clear picture of your progress and helps you stay motivated.
Practice Problems: Sharpening Your Skills
To solidify your understanding and build confidence in solving percentage problems, let's work through a few practice examples:
Practice Problem 1
35 is 25% of what number?
Solution:
- Translate the problem into an equation: 35 = 25% * x
- Convert the percentage to a decimal: 25% = 0.25
- Substitute the decimal into the equation: 35 = 0.25 * x
- Isolate x: x = 35 / 0.25
- Calculate x: x = 140
Therefore, 35 is 25% of 140.
Practice Problem 2
120 is 15% of what number?
Solution:
- Translate the problem into an equation: 120 = 15% * x
- Convert the percentage to a decimal: 15% = 0.15
- Substitute the decimal into the equation: 120 = 0.15 * x
- Isolate x: x = 120 / 0.15
- Calculate x: x = 800
Therefore, 120 is 15% of 800.
Practice Problem 3
7 is 2% of what number?
Solution:
- Translate the problem into an equation: 7 = 2% * x
- Convert the percentage to a decimal: 2% = 0.02
- Substitute the decimal into the equation: 7 = 0.02 * x
- Isolate x: x = 7 / 0.02
- Calculate x: x = 350
Therefore, 7 is 2% of 350.
By working through these practice problems, you've honed your skills in solving percentage problems and are well-prepared to tackle similar challenges in various contexts.
Conclusion: Mastering Percentages for Everyday Success
In this comprehensive guide, we've explored the question, "59 is 10% of what number?" and uncovered the underlying principles of percentages. We've learned how to convert percentages to decimals and fractions, and vice versa, and we've applied this knowledge to solve the problem using both algebraic equations and proportions.
Furthermore, we've delved into the real-world applications of percentage calculations, highlighting their relevance in financial planning, retail, sales, data analysis, and fitness. By understanding how to work with percentages, you empower yourself to make informed decisions, track your progress, and achieve your goals in various aspects of life.
Remember, practice is key to mastering any mathematical concept. So, continue to challenge yourself with percentage problems, and you'll find that these calculations become second nature. With a solid grasp of percentages, you'll be well-equipped to navigate the numerical landscape of the world around you.
