The Sum Of $5%$ Of A Number And 9 Is 16.

Introduction

In this article, we will delve into a mathematical problem that involves finding a number based on a given equation. The equation states that the sum of 5% of a number and 9 is equal to 16. We will use algebraic techniques to solve for the unknown number and explore the concept of percentages in mathematics.

Understanding the Problem

The problem can be represented mathematically as:

$$5\% \text{ of a number} + 9 = 16$$

To solve for the unknown number, we need to isolate the variable. Let's represent the unknown number as 'x'. The equation can be rewritten as:

$$0.05x + 9 = 16$$

Breaking Down the Equation

The equation consists of two parts: 5% of the number (represented by 0.05x) and a constant term (9). We need to isolate the variable 'x' by getting rid of the constant term. To do this, we can subtract 9 from both sides of the equation:

$$0.05x + 9 - 9 = 16 - 9$$

This simplifies to:

$$0.05x = 7$$

Solving for the Unknown Number

Now that we have isolated the variable 'x', we can solve for its value. To do this, we need to get rid of the coefficient 0.05. We can do this by dividing both sides of the equation by 0.05:

$$\frac{0.05x}{0.05} = \frac{7}{0.05}$$

This simplifies to:

$$x = 140$$

Conclusion

In this article, we explored a mathematical problem that involved finding a number based on a given equation. We used algebraic techniques to solve for the unknown number and explored the concept of percentages in mathematics. The solution to the problem is x = 140.

Understanding Percentages

Percentages are a way of expressing a value as a fraction of 100. In the problem, we were given 5% of a number, which is equivalent to 0.05x. To understand percentages, let's consider an example. Suppose we have a number 100 and we want to find 5% of it. We can calculate this by multiplying 100 by 0.05:

$$100 \times 0.05 = 5$$

This means that 5% of 100 is equal to 5.

Real-World Applications

Percentages have many real-world applications. For example, in finance, interest rates are often expressed as percentages. Suppose we have a savings account with a balance of $1000 and an interest rate of 5%. The interest earned on the account can be calculated by multiplying the balance by the interest rate:

$$1000 \times 0.05 = 50$$

This means that the interest earned on the account is $50.

Tips and Tricks

When working with percentages, it's essential to remember that a percentage is a fraction of 100. To convert a percentage to a decimal, simply divide the percentage by 100. For example, to convert 5% to a decimal, we can divide 5 by 100:

$$\frac{5}{100} = 0.05$$

This means that 5% is equivalent to 0.05.

Conclusion

Q&A: The Sum of 5% of a Number and 9 is 16

Q: What is the problem asking for?

A: The problem is asking for a number that, when 5% of it is added to 9, equals 16.

Q: How do I represent the problem mathematically?

A: The problem can be represented mathematically as:

$$5\% \text{ of a number} + 9 = 16$$

Q: What does 5% of a number mean?

A: 5% of a number means 5% of the number's value. To represent this mathematically, we can use the decimal equivalent of 5%, which is 0.05. So, 5% of a number can be represented as 0.05x, where x is the number.

Q: How do I solve for the unknown number?

A: To solve for the unknown number, we need to isolate the variable 'x'. We can do this by getting rid of the constant term (9) by subtracting it from both sides of the equation:

$$0.05x + 9 - 9 = 16 - 9$$

This simplifies to:

$$0.05x = 7$$

Q: How do I get rid of the coefficient 0.05?

A: To get rid of the coefficient 0.05, we can divide both sides of the equation by 0.05:

$$\frac{0.05x}{0.05} = \frac{7}{0.05}$$

This simplifies to:

$$x = 140$$

Q: What is the solution to the problem?

A: The solution to the problem is x = 140.

Q: What is the importance of understanding percentages?

A: Understanding percentages is essential in mathematics and real-world applications. Percentages are a way of expressing a value as a fraction of 100. By understanding percentages, you can solve mathematical problems and make informed decisions in finance, business, and other fields.

Q: How do I convert a percentage to a decimal?

A: To convert a percentage to a decimal, simply divide the percentage by 100. For example, to convert 5% to a decimal, we can divide 5 by 100:

$$\frac{5}{100} = 0.05$$

This means that 5% is equivalent to 0.05.

Q: What are some real-world applications of percentages?

A: Percentages have many real-world applications, including finance, business, and science. For example, interest rates are often expressed as percentages, and sales tax is typically calculated as a percentage of the purchase price.

Q: How can I practice working with percentages?

A: You can practice working with percentages by solving mathematical problems that involve percentages, such as finding 5% of a number or calculating interest rates. You can also use online resources, such as calculators and worksheets, to practice working with percentages.

Conclusion

In this article, we explored a mathematical problem that involved finding a number based on a given equation. We used algebraic techniques to solve for the unknown number and explored the concept of percentages in mathematics. We also answered common questions about the problem and provided tips and tricks for working with percentages. By following the advice outlined in this article, you can become more confident in your ability to work with percentages and solve mathematical problems.