What three numbers have an average of 142?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 142. This means if we add these three numbers together and divide by 3, we should get 142.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 142 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 142 * 3 = x + y + z
- So, the sum of our three numbers should be: 426
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 426.
Solution 1:
142, 142, 142
Verification:
(142 + 142 + 142) / 3 = 426 / 3 ≈ 142
This solution is correct!
Solution 2:
142, 142, 142
Verification:
(142 + 142 + 142) / 3 = 426 / 3 ≈ 142
This solution is correct!
Solution 3:
195, 201, 30
Verification:
(195 + 201 + 30) / 3 = 426 / 3 ≈ 142
This solution is correct!
Solution 4:
124, 26, 276
Verification:
(124 + 26 + 276) / 3 = 426 / 3 ≈ 142
This solution is correct!
Solution 5:
47, 139, 240
Verification:
(47 + 139 + 240) / 3 = 426 / 3 ≈ 142
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 426 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.