What three numbers have an average of 218?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 218. This means if we add these three numbers together and divide by 3, we should get 218.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 218 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 218 * 3 = x + y + z
- So, the sum of our three numbers should be: 654
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 654.
Solution 1:
218, 218, 218
Verification:
(218 + 218 + 218) / 3 = 654 / 3 ≈ 218
This solution is correct!
Solution 2:
218, 218, 218
Verification:
(218 + 218 + 218) / 3 = 654 / 3 ≈ 218
This solution is correct!
Solution 3:
241, 210, 203
Verification:
(241 + 210 + 203) / 3 = 654 / 3 ≈ 218
This solution is correct!
Solution 4:
416, 40, 198
Verification:
(416 + 40 + 198) / 3 = 654 / 3 ≈ 218
This solution is correct!
Solution 5:
120, 189, 345
Verification:
(120 + 189 + 345) / 3 = 654 / 3 ≈ 218
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 654 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.