What three numbers have an average of 20?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 20. This means if we add these three numbers together and divide by 3, we should get 20.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 20 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 20 * 3 = x + y + z
- So, the sum of our three numbers should be: 60
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 60.
Solution 1:
20, 20, 20
Verification:
(20 + 20 + 20) / 3 = 60 / 3 ≈ 20
This solution is correct!
Solution 2:
20, 20, 20
Verification:
(20 + 20 + 20) / 3 = 60 / 3 ≈ 20
This solution is correct!
Solution 3:
7, 16, 37
Verification:
(7 + 16 + 37) / 3 = 60 / 3 ≈ 20
This solution is correct!
Solution 4:
29, 6, 25
Verification:
(29 + 6 + 25) / 3 = 60 / 3 ≈ 20
This solution is correct!
Solution 5:
18, 7, 35
Verification:
(18 + 7 + 35) / 3 = 60 / 3 ≈ 20
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 60 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.