What three numbers have an average of 540?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 540. This means if we add these three numbers together and divide by 3, we should get 540.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 540 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 540 * 3 = x + y + z
- So, the sum of our three numbers should be: 1620
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1620.
Solution 1:
540, 540, 540
Verification:
(540 + 540 + 540) / 3 = 1620 / 3 ≈ 540
This solution is correct!
Solution 2:
540, 540, 540
Verification:
(540 + 540 + 540) / 3 = 1620 / 3 ≈ 540
This solution is correct!
Solution 3:
1507, 70, 43
Verification:
(1507 + 70 + 43) / 3 = 1620 / 3 ≈ 540
This solution is correct!
Solution 4:
993, 476, 151
Verification:
(993 + 476 + 151) / 3 = 1620 / 3 ≈ 540
This solution is correct!
Solution 5:
176, 1009, 435
Verification:
(176 + 1009 + 435) / 3 = 1620 / 3 ≈ 540
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 1620 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.