What three numbers have an average of 219?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 219. This means if we add these three numbers together and divide by 3, we should get 219.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 219 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 219 * 3 = x + y + z
- So, the sum of our three numbers should be: 657
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 657.
Solution 1:
219, 219, 219
Verification:
(219 + 219 + 219) / 3 = 657 / 3 ≈ 219
This solution is correct!
Solution 2:
219, 219, 219
Verification:
(219 + 219 + 219) / 3 = 657 / 3 ≈ 219
This solution is correct!
Solution 3:
620, 22, 15
Verification:
(620 + 22 + 15) / 3 = 657 / 3 ≈ 219
This solution is correct!
Solution 4:
402, 170, 85
Verification:
(402 + 170 + 85) / 3 = 657 / 3 ≈ 219
This solution is correct!
Solution 5:
646, 2, 9
Verification:
(646 + 2 + 9) / 3 = 657 / 3 ≈ 219
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 657 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.