What three numbers have an average of 216?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 216. This means if we add these three numbers together and divide by 3, we should get 216.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 216 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 216 * 3 = x + y + z
- So, the sum of our three numbers should be: 648
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 648.
Solution 1:
216, 216, 216
Verification:
(216 + 216 + 216) / 3 = 648 / 3 ≈ 216
This solution is correct!
Solution 2:
216, 216, 216
Verification:
(216 + 216 + 216) / 3 = 648 / 3 ≈ 216
This solution is correct!
Solution 3:
39, 111, 498
Verification:
(39 + 111 + 498) / 3 = 648 / 3 ≈ 216
This solution is correct!
Solution 4:
1, 502, 145
Verification:
(1 + 502 + 145) / 3 = 648 / 3 ≈ 216
This solution is correct!
Solution 5:
378, 227, 43
Verification:
(378 + 227 + 43) / 3 = 648 / 3 ≈ 216
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 648 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.