What three numbers have an average of 5?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 5. This means if we add these three numbers together and divide by 3, we should get 5.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 5 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 5 * 3 = x + y + z
- So, the sum of our three numbers should be: 15
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 15.
Solution 1:
5, 5, 5
Verification:
(5 + 5 + 5) / 3 = 15 / 3 ≈ 5
This solution is correct!
Solution 2:
5, 5, 5
Verification:
(5 + 5 + 5) / 3 = 15 / 3 ≈ 5
This solution is correct!
Solution 3:
1, 3, 11
Verification:
(1 + 3 + 11) / 3 = 15 / 3 ≈ 5
This solution is correct!
Solution 4:
13, 1, 1
Verification:
(13 + 1 + 1) / 3 = 15 / 3 ≈ 5
This solution is correct!
Solution 5:
8, 2, 5
Verification:
(8 + 2 + 5) / 3 = 15 / 3 ≈ 5
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 15 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.