What three numbers have an average of 23?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 23. This means if we add these three numbers together and divide by 3, we should get 23.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 23 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 23 * 3 = x + y + z
- So, the sum of our three numbers should be: 69
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 69.
Solution 1:
23, 23, 23
Verification:
(23 + 23 + 23) / 3 = 69 / 3 ≈ 23
This solution is correct!
Solution 2:
23, 23, 23
Verification:
(23 + 23 + 23) / 3 = 69 / 3 ≈ 23
This solution is correct!
Solution 3:
50, 2, 17
Verification:
(50 + 2 + 17) / 3 = 69 / 3 ≈ 23
This solution is correct!
Solution 4:
33, 9, 27
Verification:
(33 + 9 + 27) / 3 = 69 / 3 ≈ 23
This solution is correct!
Solution 5:
8, 2, 59
Verification:
(8 + 2 + 59) / 3 = 69 / 3 ≈ 23
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 69 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.