What three numbers have an average of 361?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 361. This means if we add these three numbers together and divide by 3, we should get 361.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 361 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 361 * 3 = x + y + z
- So, the sum of our three numbers should be: 1083
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1083.
Solution 1:
361, 361, 361
Verification:
(361 + 361 + 361) / 3 = 1083 / 3 ≈ 361
This solution is correct!
Solution 2:
361, 361, 361
Verification:
(361 + 361 + 361) / 3 = 1083 / 3 ≈ 361
This solution is correct!
Solution 3:
552, 493, 38
Verification:
(552 + 493 + 38) / 3 = 1083 / 3 ≈ 361
This solution is correct!
Solution 4:
838, 142, 103
Verification:
(838 + 142 + 103) / 3 = 1083 / 3 ≈ 361
This solution is correct!
Solution 5:
681, 181, 221
Verification:
(681 + 181 + 221) / 3 = 1083 / 3 ≈ 361
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 1083 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.