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:
1018, 28, 40
Verification:
(1018 + 28 + 40) / 3 = 1086 / 3 ≈ 362
This solution is correct!
Solution 4:
137, 766, 183
Verification:
(137 + 766 + 183) / 3 = 1086 / 3 ≈ 362
This solution is correct!
Solution 5:
390, 492, 204
Verification:
(390 + 492 + 204) / 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.