What three numbers have an average of 695?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 695. This means if we add these three numbers together and divide by 3, we should get 695.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 695 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 695 * 3 = x + y + z
- So, the sum of our three numbers should be: 2085
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2085.
Solution 1:
695, 695, 695
Verification:
(695 + 695 + 695) / 3 = 2085 / 3 ≈ 695
This solution is correct!
Solution 2:
695, 695, 695
Verification:
(695 + 695 + 695) / 3 = 2085 / 3 ≈ 695
This solution is correct!
Solution 3:
1193, 850, 42
Verification:
(1193 + 850 + 42) / 3 = 2085 / 3 ≈ 695
This solution is correct!
Solution 4:
403, 1475, 207
Verification:
(403 + 1475 + 207) / 3 = 2085 / 3 ≈ 695
This solution is correct!
Solution 5:
821, 252, 1012
Verification:
(821 + 252 + 1012) / 3 = 2085 / 3 ≈ 695
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 2085 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.