What three numbers have an average of 365?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 365. This means if we add these three numbers together and divide by 3, we should get 365.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 365 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 365 * 3 = x + y + z
- So, the sum of our three numbers should be: 1095
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1095.
Solution 1:
365, 365, 365
Verification:
(365 + 365 + 365) / 3 = 1095 / 3 ≈ 365
This solution is correct!
Solution 2:
365, 365, 365
Verification:
(365 + 365 + 365) / 3 = 1095 / 3 ≈ 365
This solution is correct!
Solution 3:
787, 185, 123
Verification:
(787 + 185 + 123) / 3 = 1095 / 3 ≈ 365
This solution is correct!
Solution 4:
260, 260, 575
Verification:
(260 + 260 + 575) / 3 = 1095 / 3 ≈ 365
This solution is correct!
Solution 5:
312, 283, 500
Verification:
(312 + 283 + 500) / 3 = 1095 / 3 ≈ 365
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 1095 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.