What three numbers have an average of 563?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 563. This means if we add these three numbers together and divide by 3, we should get 563.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 563 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 563 * 3 = x + y + z
- So, the sum of our three numbers should be: 1689
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1689.
Solution 1:
563, 563, 563
Verification:
(563 + 563 + 563) / 3 = 1689 / 3 ≈ 563
This solution is correct!
Solution 2:
563, 563, 563
Verification:
(563 + 563 + 563) / 3 = 1689 / 3 ≈ 563
This solution is correct!
Solution 3:
320, 902, 467
Verification:
(320 + 902 + 467) / 3 = 1689 / 3 ≈ 563
This solution is correct!
Solution 4:
516, 1082, 91
Verification:
(516 + 1082 + 91) / 3 = 1689 / 3 ≈ 563
This solution is correct!
Solution 5:
1595, 88, 6
Verification:
(1595 + 88 + 6) / 3 = 1689 / 3 ≈ 563
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 1689 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.