What three numbers have an average of 456?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 456. This means if we add these three numbers together and divide by 3, we should get 456.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 456 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 456 * 3 = x + y + z
- So, the sum of our three numbers should be: 1368
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1368.
Solution 1:
456, 456, 456
Verification:
(456 + 456 + 456) / 3 = 1368 / 3 ≈ 456
This solution is correct!
Solution 2:
456, 456, 456
Verification:
(456 + 456 + 456) / 3 = 1368 / 3 ≈ 456
This solution is correct!
Solution 3:
587, 221, 560
Verification:
(587 + 221 + 560) / 3 = 1368 / 3 ≈ 456
This solution is correct!
Solution 4:
241, 46, 1081
Verification:
(241 + 46 + 1081) / 3 = 1368 / 3 ≈ 456
This solution is correct!
Solution 5:
1089, 253, 26
Verification:
(1089 + 253 + 26) / 3 = 1368 / 3 ≈ 456
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 1368 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.