What three numbers have an average of 214?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 214. This means if we add these three numbers together and divide by 3, we should get 214.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 214 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 214 * 3 = x + y + z
- So, the sum of our three numbers should be: 642
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 642.
Solution 1:
214, 214, 214
Verification:
(214 + 214 + 214) / 3 = 642 / 3 ≈ 214
This solution is correct!
Solution 2:
214, 214, 214
Verification:
(214 + 214 + 214) / 3 = 642 / 3 ≈ 214
This solution is correct!
Solution 3:
6, 602, 34
Verification:
(6 + 602 + 34) / 3 = 642 / 3 ≈ 214
This solution is correct!
Solution 4:
176, 191, 275
Verification:
(176 + 191 + 275) / 3 = 642 / 3 ≈ 214
This solution is correct!
Solution 5:
529, 8, 105
Verification:
(529 + 8 + 105) / 3 = 642 / 3 ≈ 214
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 642 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.