What three numbers have an average of 215?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 215. This means if we add these three numbers together and divide by 3, we should get 215.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 215 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 215 * 3 = x + y + z
- So, the sum of our three numbers should be: 645
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 645.
Solution 1:
215, 215, 215
Verification:
(215 + 215 + 215) / 3 = 645 / 3 ≈ 215
This solution is correct!
Solution 2:
215, 215, 215
Verification:
(215 + 215 + 215) / 3 = 645 / 3 ≈ 215
This solution is correct!
Solution 3:
84, 69, 492
Verification:
(84 + 69 + 492) / 3 = 645 / 3 ≈ 215
This solution is correct!
Solution 4:
608, 3, 34
Verification:
(608 + 3 + 34) / 3 = 645 / 3 ≈ 215
This solution is correct!
Solution 5:
419, 138, 88
Verification:
(419 + 138 + 88) / 3 = 645 / 3 ≈ 215
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 645 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.