What three numbers have an average of 895?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 895. This means if we add these three numbers together and divide by 3, we should get 895.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 895 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 895 * 3 = x + y + z
- So, the sum of our three numbers should be: 2685
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2685.
Solution 1:
895, 895, 895
Verification:
(895 + 895 + 895) / 3 = 2685 / 3 ≈ 895
This solution is correct!
Solution 2:
895, 895, 895
Verification:
(895 + 895 + 895) / 3 = 2685 / 3 ≈ 895
This solution is correct!
Solution 3:
1046, 1585, 54
Verification:
(1046 + 1585 + 54) / 3 = 2685 / 3 ≈ 895
This solution is correct!
Solution 4:
2059, 134, 492
Verification:
(2059 + 134 + 492) / 3 = 2685 / 3 ≈ 895
This solution is correct!
Solution 5:
2086, 297, 302
Verification:
(2086 + 297 + 302) / 3 = 2685 / 3 ≈ 895
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 2685 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.