Finding the Missing Number When the Mean of Two Numbers is Known

When working with the mean of two numbers, it's often a straightforward task. If the mean of two numbers is given, and one number is known, you can find the other. This article explains the process step-by-step, ensuring it's easy for students to understand and SEO-friendly for web searches.

About Mean and Average

The mean (or average) of a set of numbers is calculated by summing all the numbers and then dividing by the count of numbers. In this case, we are dealing with the mean of two numbers. The formula for the mean of two numbers, (a) and (b), is given as:

[text{Mean} frac{a b}{2}]In a typical problem, you might be given the mean and one of the numbers, and you need to find the other. Let's explore a common scenario where the mean of two numbers is 15, and one of the numbers is 18.

Problem Description

Consider the problem where the mean of two numbers is 15, and one of the numbers is 18. The goal is to find the missing number.

Solution

Let's denote the missing number as (x). The mean of the two numbers is given as 15. Therefore, we can set up the equation:

[frac{18 x}{2} 15]Multiplying both sides by 2 to clear the denominator gives:

[18 x 30]Subtracting 18 from both sides provides the value of (x):

[x 30 - 18 12]Therefore, the missing number is 12. Let's also verify the result by checking the mean of 18 and 12:

[frac{18 12}{2} frac{30}{2} 15]This confirms that our solution is correct.

Alternatively, you could approach this problem by recognizing that the total of the two numbers must be twice the mean. That is:

[15 times 2 30]With one number being 18, the other number must be:

[30 - 18 12]This straightforward method quickly gives the same result, verifying the initial solution.

Key Concepts

The concepts explained here are fundamental in algebra and arithmetic. Understanding these can help in solving similar problems more efficiently. Some key takeaways from this problem are:

1. **Mean and Total**: The product of the mean and the number of items gives the total.

2. **Algebraic Manipulation**: Setting up an equation and solving it is a powerful tool for problem-solving.

3. **Verification**: Verifying the solution by plugging the found value back into the original problem is a good practice to ensure accuracy.

Conclusion

By following these steps, you can easily find the missing number when the mean of two numbers is known. This skill is not only useful for academic purposes but also in various real-world scenarios where you need to calculate averages.

If you need more practice or are preparing for a specific test, consider exploring more examples of similar problems in textbooks or online resources. Just remember that a clear understanding of basic concepts is the foundation for success in more complex mathematical tasks.