What three numbers have an average of 411?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 411. This means if we add these three numbers together and divide by 3, we should get 411.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 411 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 411 * 3 = x + y + z
- So, the sum of our three numbers should be: 1233
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1233.
Solution 1:
411, 411, 411
Verification:
(411 + 411 + 411) / 3 = 1233 / 3 ≈ 411
This solution is correct!
Solution 2:
411, 411, 411
Verification:
(411 + 411 + 411) / 3 = 1233 / 3 ≈ 411
This solution is correct!
Solution 3:
525, 580, 128
Verification:
(525 + 580 + 128) / 3 = 1233 / 3 ≈ 411
This solution is correct!
Solution 4:
1231, 1, 1
Verification:
(1231 + 1 + 1) / 3 = 1233 / 3 ≈ 411
This solution is correct!
Solution 5:
657, 447, 129
Verification:
(657 + 447 + 129) / 3 = 1233 / 3 ≈ 411
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 1233 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.