What three numbers have an average of 366?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 366. This means if we add these three numbers together and divide by 3, we should get 366.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 366 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 366 * 3 = x + y + z
- So, the sum of our three numbers should be: 1098
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1098.
Solution 1:
366, 366, 366
Verification:
(366 + 366 + 366) / 3 = 1098 / 3 ≈ 366
This solution is correct!
Solution 2:
366, 366, 366
Verification:
(366 + 366 + 366) / 3 = 1098 / 3 ≈ 366
This solution is correct!
Solution 3:
280, 121, 697
Verification:
(280 + 121 + 697) / 3 = 1098 / 3 ≈ 366
This solution is correct!
Solution 4:
660, 404, 34
Verification:
(660 + 404 + 34) / 3 = 1098 / 3 ≈ 366
This solution is correct!
Solution 5:
489, 18, 591
Verification:
(489 + 18 + 591) / 3 = 1098 / 3 ≈ 366
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 1098 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.