What three numbers have an average of 546?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 546. This means if we add these three numbers together and divide by 3, we should get 546.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 546 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 546 * 3 = x + y + z
- So, the sum of our three numbers should be: 1638
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1638.
Solution 1:
546, 546, 546
Verification:
(546 + 546 + 546) / 3 = 1638 / 3 ≈ 546
This solution is correct!
Solution 2:
546, 546, 546
Verification:
(546 + 546 + 546) / 3 = 1638 / 3 ≈ 546
This solution is correct!
Solution 3:
1030, 206, 402
Verification:
(1030 + 206 + 402) / 3 = 1638 / 3 ≈ 546
This solution is correct!
Solution 4:
1141, 441, 56
Verification:
(1141 + 441 + 56) / 3 = 1638 / 3 ≈ 546
This solution is correct!
Solution 5:
247, 355, 1036
Verification:
(247 + 355 + 1036) / 3 = 1638 / 3 ≈ 546
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 1638 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.