What three numbers have an average of 640?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 640. This means if we add these three numbers together and divide by 3, we should get 640.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 640 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 640 * 3 = x + y + z
- So, the sum of our three numbers should be: 1920
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1920.
Solution 1:
640, 640, 640
Verification:
(640 + 640 + 640) / 3 = 1920 / 3 ≈ 640
This solution is correct!
Solution 2:
640, 640, 640
Verification:
(640 + 640 + 640) / 3 = 1920 / 3 ≈ 640
This solution is correct!
Solution 3:
898, 734, 288
Verification:
(898 + 734 + 288) / 3 = 1920 / 3 ≈ 640
This solution is correct!
Solution 4:
505, 123, 1292
Verification:
(505 + 123 + 1292) / 3 = 1920 / 3 ≈ 640
This solution is correct!
Solution 5:
910, 35, 975
Verification:
(910 + 35 + 975) / 3 = 1920 / 3 ≈ 640
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 1920 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.