What three numbers have an average of 543?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 543. This means if we add these three numbers together and divide by 3, we should get 543.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 543 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 543 * 3 = x + y + z
- So, the sum of our three numbers should be: 1629
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1629.
Solution 1:
543, 543, 543
Verification:
(543 + 543 + 543) / 3 = 1629 / 3 ≈ 543
This solution is correct!
Solution 2:
543, 543, 543
Verification:
(543 + 543 + 543) / 3 = 1629 / 3 ≈ 543
This solution is correct!
Solution 3:
861, 585, 183
Verification:
(861 + 585 + 183) / 3 = 1629 / 3 ≈ 543
This solution is correct!
Solution 4:
1488, 123, 18
Verification:
(1488 + 123 + 18) / 3 = 1629 / 3 ≈ 543
This solution is correct!
Solution 5:
1254, 229, 146
Verification:
(1254 + 229 + 146) / 3 = 1629 / 3 ≈ 543
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 1629 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.