What three numbers have an average of 362?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 362. This means if we add these three numbers together and divide by 3, we should get 362.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 362 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 362 * 3 = x + y + z
- So, the sum of our three numbers should be: 1086
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1086.
Solution 1:
362, 362, 362
Verification:
(362 + 362 + 362) / 3 = 1086 / 3 ≈ 362
This solution is correct!
Solution 2:
362, 362, 362
Verification:
(362 + 362 + 362) / 3 = 1086 / 3 ≈ 362
This solution is correct!
Solution 3:
379, 447, 260
Verification:
(379 + 447 + 260) / 3 = 1086 / 3 ≈ 362
This solution is correct!
Solution 4:
98, 265, 723
Verification:
(98 + 265 + 723) / 3 = 1086 / 3 ≈ 362
This solution is correct!
Solution 5:
320, 275, 491
Verification:
(320 + 275 + 491) / 3 = 1086 / 3 ≈ 362
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 1086 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.