What three numbers have an average of 367?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 367. This means if we add these three numbers together and divide by 3, we should get 367.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 367 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 367 * 3 = x + y + z
- So, the sum of our three numbers should be: 1101
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1101.
Solution 1:
367, 367, 367
Verification:
(367 + 367 + 367) / 3 = 1101 / 3 ≈ 367
This solution is correct!
Solution 2:
367, 367, 367
Verification:
(367 + 367 + 367) / 3 = 1101 / 3 ≈ 367
This solution is correct!
Solution 3:
916, 74, 111
Verification:
(916 + 74 + 111) / 3 = 1101 / 3 ≈ 367
This solution is correct!
Solution 4:
304, 686, 111
Verification:
(304 + 686 + 111) / 3 = 1101 / 3 ≈ 367
This solution is correct!
Solution 5:
858, 111, 132
Verification:
(858 + 111 + 132) / 3 = 1101 / 3 ≈ 367
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 1101 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.