What three numbers have an average of 342?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 342. This means if we add these three numbers together and divide by 3, we should get 342.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 342 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 342 * 3 = x + y + z
- So, the sum of our three numbers should be: 1026
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1026.
Solution 1:
342, 342, 342
Verification:
(342 + 342 + 342) / 3 = 1026 / 3 ≈ 342
This solution is correct!
Solution 2:
342, 342, 342
Verification:
(342 + 342 + 342) / 3 = 1026 / 3 ≈ 342
This solution is correct!
Solution 3:
70, 158, 798
Verification:
(70 + 158 + 798) / 3 = 1026 / 3 ≈ 342
This solution is correct!
Solution 4:
689, 142, 195
Verification:
(689 + 142 + 195) / 3 = 1026 / 3 ≈ 342
This solution is correct!
Solution 5:
69, 354, 603
Verification:
(69 + 354 + 603) / 3 = 1026 / 3 ≈ 342
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 1026 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.