What three numbers have an average of 468?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 468. This means if we add these three numbers together and divide by 3, we should get 468.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 468 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 468 * 3 = x + y + z
- So, the sum of our three numbers should be: 1404
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1404.
Solution 1:
468, 468, 468
Verification:
(468 + 468 + 468) / 3 = 1404 / 3 ≈ 468
This solution is correct!
Solution 2:
468, 468, 468
Verification:
(468 + 468 + 468) / 3 = 1404 / 3 ≈ 468
This solution is correct!
Solution 3:
428, 676, 300
Verification:
(428 + 676 + 300) / 3 = 1404 / 3 ≈ 468
This solution is correct!
Solution 4:
239, 198, 967
Verification:
(239 + 198 + 967) / 3 = 1404 / 3 ≈ 468
This solution is correct!
Solution 5:
166, 1078, 160
Verification:
(166 + 1078 + 160) / 3 = 1404 / 3 ≈ 468
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 1404 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.