What three numbers have an average of 440?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 440. This means if we add these three numbers together and divide by 3, we should get 440.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 440 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 440 * 3 = x + y + z
- So, the sum of our three numbers should be: 1320
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1320.
Solution 1:
440, 440, 440
Verification:
(440 + 440 + 440) / 3 = 1320 / 3 ≈ 440
This solution is correct!
Solution 2:
440, 440, 440
Verification:
(440 + 440 + 440) / 3 = 1320 / 3 ≈ 440
This solution is correct!
Solution 3:
816, 5, 499
Verification:
(816 + 5 + 499) / 3 = 1320 / 3 ≈ 440
This solution is correct!
Solution 4:
933, 166, 221
Verification:
(933 + 166 + 221) / 3 = 1320 / 3 ≈ 440
This solution is correct!
Solution 5:
306, 532, 482
Verification:
(306 + 532 + 482) / 3 = 1320 / 3 ≈ 440
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 1320 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.