The average of five numbers is 24. If four of the numbers are 18, 22, 26, and 30, what is the fifth number?
["The Average of Five Numbers Is 24 — How to Find the Fifth Number (Step-by-Step Explanation)", "When you learn that the average of five numbers is 24, it means that if you add all five numbers together and divide by 5, the result is 24. This straightforward concept is a powerful tool in algebra, problem-solving, and data analysis. In this article, we’ll break down how to find the missing fifth number when four out of the five numbers are known — specifically, 18, 22, 26, and 30 — and what the average of 24 tells us.", "---", "### What Does the Average Mean?", "The average (or mean) of a set of numbers is calculated using the formula:", "[\n\ ext{Average} = \frac{\ ext{Sum of all numbers}}{\ ext{Number of values}}\n]", "In this case:", "[\n24 = \frac{18 + 22 + 26 + 30 + x}{5}\n]", "where ( x ) is the unknown fifth number.", "---", "### Step 1: Calculate the Known Sum", "First, add the four known numbers:", "[\n18 + 22 + 26 + 30 = 96\n]", "---", "### Step 2: Use the Average Formula to Find Total Sum", "Since the average is 24 for five numbers:", "[\n\frac{96 + x}{5} = 24\n]", "Multiply both sides by 5 to eliminate the denominator:", "[\n96 + x = 120\n]", "---", "### Step 3: Solve for ( x )", "Subtract 96 from both sides:", "[\nx = 120 - 96 = 24\n]", "---", "### ✅ Final Answer: The fifth number is 24", "So, given the numbers 18, 22, 26, 30, and unknown ( x ), if the average of all five is 24, the missing number must be 24.", "---", "### Why This Matters", "Understanding how averages work is essential not only in math but also in real-life scenarios like budgeting, grades, and performance metrics. Knowing how to find missing values in a dataset helps you interpret and analyze information more effectively.", "---", "### Key Takeaways:", "- Average = Total Sum ÷ Number of Values\n- To find a missing number given the average and some values, use:\n [\n \ ext{Missing number} = (\ ext{Average} \ imes \ ext{Total count}) - \ ext{Sum of known values}\n ]\n- This method applies broadly to math problems, statistics, and data analysis.", "---", "Want to master averages and related math concepts? Check out more tutorials on arithmetic mean, data interpretation, and problem-solving strategies!"]
