The Sum Of Three Consecutive Counting Numbers Is 99. What Are The Three Counting Numbers?

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Introduction

In mathematics, a counting number is a positive integer that is used to count objects or quantities. Consecutive counting numbers are numbers that follow each other in order, such as 1, 2, 3, or 10, 11, 12. In this article, we will explore the problem of finding three consecutive counting numbers that sum up to 99.

Understanding the Problem

The problem states that the sum of three consecutive counting numbers is 99. This means that we need to find three numbers in a row, such as x, x+1, and x+2, that add up to 99. For example, if we let x = 1, then the three consecutive numbers would be 1, 2, and 3, which add up to 6, not 99.

Setting Up the Equation

To solve this problem, we can set up an equation based on the given information. Let's assume that the three consecutive counting numbers are x, x+1, and x+2. We know that their sum is 99, so we can write the equation:

x + (x+1) + (x+2) = 99

Simplifying the Equation

To simplify the equation, we can combine like terms:

3x + 3 = 99

Solving for x

Now, we can solve for x by subtracting 3 from both sides of the equation:

3x = 96

Next, we can divide both sides of the equation by 3:

x = 32

Finding the Three Consecutive Counting Numbers

Now that we have found the value of x, we can find the three consecutive counting numbers. Since x = 32, the three consecutive numbers are:

32, 33, and 34

Verifying the Solution

To verify our solution, we can add up the three consecutive numbers:

32 + 33 + 34 = 99

This confirms that our solution is correct.

Conclusion

In this article, we explored the problem of finding three consecutive counting numbers that sum up to 99. We set up an equation based on the given information, simplified the equation, and solved for x. We then found the three consecutive counting numbers and verified our solution. The three consecutive counting numbers that sum up to 99 are 32, 33, and 34.

Additional Examples

Here are a few additional examples of finding three consecutive counting numbers that sum up to a given number:

  • The sum of three consecutive counting numbers is 120. What are the three counting numbers?
  • The sum of three consecutive counting numbers is 180. What are the three counting numbers?
  • The sum of three consecutive counting numbers is 240. What are the three counting numbers?

Tips and Tricks

Here are a few tips and tricks for solving problems like this:

  • Always read the problem carefully and understand what is being asked.
  • Set up an equation based on the given information.
  • Simplify the equation by combining like terms.
  • Solve for the variable by isolating it on one side of the equation.
  • Verify your solution by plugging it back into the original equation.

Real-World Applications

This type of problem has many real-world applications, such as:

  • Finance: Finding the sum of three consecutive years' worth of expenses or revenues.
  • Science: Finding the sum of three consecutive measurements or readings.
  • Engineering: Finding the sum of three consecutive values of a physical quantity, such as temperature or pressure.

Conclusion

In conclusion, finding three consecutive counting numbers that sum up to a given number is a mathematical problem that can be solved using algebraic techniques. By setting up an equation, simplifying it, and solving for the variable, we can find the three consecutive counting numbers. This type of problem has many real-world applications and can be used to model a variety of situations.

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Q: What are counting numbers?

A: Counting numbers are positive integers that are used to count objects or quantities. They are also known as natural numbers.

Q: What are consecutive counting numbers?

A: Consecutive counting numbers are numbers that follow each other in order, such as 1, 2, 3, or 10, 11, 12.

Q: How do I find the sum of three consecutive counting numbers?

A: To find the sum of three consecutive counting numbers, you can set up an equation based on the given information. Let's assume that the three consecutive counting numbers are x, x+1, and x+2. We know that their sum is 99, so we can write the equation:

x + (x+1) + (x+2) = 99

Q: What if I don't know the value of x?

A: If you don't know the value of x, you can use algebraic techniques to solve for it. To simplify the equation, you can combine like terms:

3x + 3 = 99

Next, you can subtract 3 from both sides of the equation:

3x = 96

Then, you can divide both sides of the equation by 3:

x = 32

Q: How do I verify my solution?

A: To verify your solution, you can add up the three consecutive numbers:

32 + 33 + 34 = 99

This confirms that your solution is correct.

Q: What if I want to find the sum of three consecutive counting numbers that is not 99?

A: If you want to find the sum of three consecutive counting numbers that is not 99, you can use the same algebraic techniques to solve for x. For example, if you want to find the sum of three consecutive counting numbers that is 120, you can set up the equation:

x + (x+1) + (x+2) = 120

Simplifying the equation, you get:

3x + 3 = 120

Subtracting 3 from both sides of the equation, you get:

3x = 117

Dividing both sides of the equation by 3, you get:

x = 39

Q: Can I use this technique to find the sum of more than three consecutive counting numbers?

A: Yes, you can use this technique to find the sum of more than three consecutive counting numbers. For example, if you want to find the sum of four consecutive counting numbers, you can set up the equation:

x + (x+1) + (x+2) + (x+3) = 120

Simplifying the equation, you get:

4x + 6 = 120

Subtracting 6 from both sides of the equation, you get:

4x = 114

Dividing both sides of the equation by 4, you get:

x = 28.5

Q: What are some real-world applications of this technique?

A: This technique has many real-world applications, such as:

  • Finance: Finding the sum of three consecutive years' worth of expenses or revenues.
  • Science: Finding the sum of three consecutive measurements or readings.
  • Engineering: Finding the sum of three consecutive values of a physical quantity, such as temperature or pressure.

Q: Can I use this technique to solve other types of problems?

A: Yes, you can use this technique to solve other types of problems that involve finding the sum of consecutive numbers. For example, you can use this technique to find the sum of consecutive even or odd numbers.

Q: What are some common mistakes to avoid when using this technique?

A: Some common mistakes to avoid when using this technique include:

  • Not reading the problem carefully and understanding what is being asked.
  • Not setting up the equation correctly.
  • Not simplifying the equation correctly.
  • Not solving for the variable correctly.

Q: How can I practice using this technique?

A: You can practice using this technique by working through examples and exercises. You can also try using this technique to solve real-world problems.