What three numbers have an average of 648?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 648. This means if we add these three numbers together and divide by 3, we should get 648.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 648 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 648 * 3 = x + y + z
- So, the sum of our three numbers should be: 1944
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1944.
Solution 1:
648, 648, 648
Verification:
(648 + 648 + 648) / 3 = 1944 / 3 ≈ 648
This solution is correct!
Solution 2:
648, 648, 648
Verification:
(648 + 648 + 648) / 3 = 1944 / 3 ≈ 648
This solution is correct!
Solution 3:
1379, 542, 23
Verification:
(1379 + 542 + 23) / 3 = 1944 / 3 ≈ 648
This solution is correct!
Solution 4:
242, 234, 1468
Verification:
(242 + 234 + 1468) / 3 = 1944 / 3 ≈ 648
This solution is correct!
Solution 5:
1331, 551, 62
Verification:
(1331 + 551 + 62) / 3 = 1944 / 3 ≈ 648
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 1944 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.