What three numbers have an average of 13?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 13. This means if we add these three numbers together and divide by 3, we should get 13.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 13 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 13 * 3 = x + y + z
- So, the sum of our three numbers should be: 39
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 39.
Solution 1:
13, 13, 13
Verification:
(13 + 13 + 13) / 3 = 39 / 3 ≈ 13
This solution is correct!
Solution 2:
13, 13, 13
Verification:
(13 + 13 + 13) / 3 = 39 / 3 ≈ 13
This solution is correct!
Solution 3:
37, 1, 1
Verification:
(37 + 1 + 1) / 3 = 39 / 3 ≈ 13
This solution is correct!
Solution 4:
1, 22, 16
Verification:
(1 + 22 + 16) / 3 = 39 / 3 ≈ 13
This solution is correct!
Solution 5:
6, 2, 31
Verification:
(6 + 2 + 31) / 3 = 39 / 3 ≈ 13
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 39 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.