What three numbers have an average of 50?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 50. This means if we add these three numbers together and divide by 3, we should get 50.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 50 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 50 * 3 = x + y + z
- So, the sum of our three numbers should be: 150
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 150.
Solution 1:
50, 50, 50
Verification:
(50 + 50 + 50) / 3 = 150 / 3 ≈ 50
This solution is correct!
Solution 2:
50, 50, 50
Verification:
(50 + 50 + 50) / 3 = 150 / 3 ≈ 50
This solution is correct!
Solution 3:
21, 108, 21
Verification:
(21 + 108 + 21) / 3 = 150 / 3 ≈ 50
This solution is correct!
Solution 4:
59, 74, 17
Verification:
(59 + 74 + 17) / 3 = 150 / 3 ≈ 50
This solution is correct!
Solution 5:
26, 107, 17
Verification:
(26 + 107 + 17) / 3 = 150 / 3 ≈ 50
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 150 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.