What three numbers have an average of 567?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 567. This means if we add these three numbers together and divide by 3, we should get 567.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 567 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 567 * 3 = x + y + z
- So, the sum of our three numbers should be: 1701
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1701.
Solution 1:
567, 567, 567
Verification:
(567 + 567 + 567) / 3 = 1701 / 3 ≈ 567
This solution is correct!
Solution 2:
567, 567, 567
Verification:
(567 + 567 + 567) / 3 = 1701 / 3 ≈ 567
This solution is correct!
Solution 3:
1218, 150, 333
Verification:
(1218 + 150 + 333) / 3 = 1701 / 3 ≈ 567
This solution is correct!
Solution 4:
1172, 521, 8
Verification:
(1172 + 521 + 8) / 3 = 1701 / 3 ≈ 567
This solution is correct!
Solution 5:
695, 42, 964
Verification:
(695 + 42 + 964) / 3 = 1701 / 3 ≈ 567
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 1701 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.