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:
1917, 205, 563
Verification:
(1917 + 205 + 563) / 3 = 2685 / 3 ≈ 895
This solution is correct!
Solution 4:
1973, 22, 690
Verification:
(1973 + 22 + 690) / 3 = 2685 / 3 ≈ 895
This solution is correct!
Solution 5:
1280, 1084, 321
Verification:
(1280 + 1084 + 321) / 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.