What three numbers have an average of 850?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 850. This means if we add these three numbers together and divide by 3, we should get 850.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 850 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 850 * 3 = x + y + z
- So, the sum of our three numbers should be: 2550
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2550.
Solution 1:
850, 850, 850
Verification:
(850 + 850 + 850) / 3 = 2550 / 3 ≈ 850
This solution is correct!
Solution 2:
850, 850, 850
Verification:
(850 + 850 + 850) / 3 = 2550 / 3 ≈ 850
This solution is correct!
Solution 3:
1709, 628, 213
Verification:
(1709 + 628 + 213) / 3 = 2550 / 3 ≈ 850
This solution is correct!
Solution 4:
2211, 86, 253
Verification:
(2211 + 86 + 253) / 3 = 2550 / 3 ≈ 850
This solution is correct!
Solution 5:
1872, 614, 64
Verification:
(1872 + 614 + 64) / 3 = 2550 / 3 ≈ 850
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 2550 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.