What three numbers have an average of 650?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 650. This means if we add these three numbers together and divide by 3, we should get 650.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 650 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 650 * 3 = x + y + z
- So, the sum of our three numbers should be: 1950
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1950.
Solution 1:
650, 650, 650
Verification:
(650 + 650 + 650) / 3 = 1950 / 3 ≈ 650
This solution is correct!
Solution 2:
650, 650, 650
Verification:
(650 + 650 + 650) / 3 = 1950 / 3 ≈ 650
This solution is correct!
Solution 3:
269, 1642, 39
Verification:
(269 + 1642 + 39) / 3 = 1950 / 3 ≈ 650
This solution is correct!
Solution 4:
1522, 426, 2
Verification:
(1522 + 426 + 2) / 3 = 1950 / 3 ≈ 650
This solution is correct!
Solution 5:
427, 163, 1360
Verification:
(427 + 163 + 1360) / 3 = 1950 / 3 ≈ 650
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 1950 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.