What three numbers have an average of 21?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 21. This means if we add these three numbers together and divide by 3, we should get 21.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 21 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 21 * 3 = x + y + z
- So, the sum of our three numbers should be: 63
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 63.
Solution 1:
21, 21, 21
Verification:
(21 + 21 + 21) / 3 = 63 / 3 ≈ 21
This solution is correct!
Solution 2:
21, 21, 21
Verification:
(21 + 21 + 21) / 3 = 63 / 3 ≈ 21
This solution is correct!
Solution 3:
5, 15, 43
Verification:
(5 + 15 + 43) / 3 = 63 / 3 ≈ 21
This solution is correct!
Solution 4:
55, 7, 1
Verification:
(55 + 7 + 1) / 3 = 63 / 3 ≈ 21
This solution is correct!
Solution 5:
13, 40, 10
Verification:
(13 + 40 + 10) / 3 = 63 / 3 ≈ 21
This solution is correct!
Explanation:
As you can see, there are many possible solutions. We can find more by:
- Choosing any two numbers
- Subtracting their sum from 63 to get the third number
Remember:
- The numbers don't have to be whole numbers.
- They can even be negative (although that might not make sense in some real-world contexts).
- The order of the numbers doesn't matter for the average.