What three numbers have an average of 426?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 426. This means if we add these three numbers together and divide by 3, we should get 426.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 426 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 426 * 3 = x + y + z
- So, the sum of our three numbers should be: 1278
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1278.
Solution 1:
426, 426, 426
Verification:
(426 + 426 + 426) / 3 = 1278 / 3 ≈ 426
This solution is correct!
Solution 2:
426, 426, 426
Verification:
(426 + 426 + 426) / 3 = 1278 / 3 ≈ 426
This solution is correct!
Solution 3:
645, 336, 297
Verification:
(645 + 336 + 297) / 3 = 1278 / 3 ≈ 426
This solution is correct!
Solution 4:
601, 396, 281
Verification:
(601 + 396 + 281) / 3 = 1278 / 3 ≈ 426
This solution is correct!
Solution 5:
159, 547, 572
Verification:
(159 + 547 + 572) / 3 = 1278 / 3 ≈ 426
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 1278 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.