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:
971, 807, 172
Verification:
(971 + 807 + 172) / 3 = 1950 / 3 ≈ 650
This solution is correct!
Solution 4:
58, 1165, 727
Verification:
(58 + 1165 + 727) / 3 = 1950 / 3 ≈ 650
This solution is correct!
Solution 5:
120, 314, 1516
Verification:
(120 + 314 + 1516) / 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.