What three numbers have an average of 897?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 897. This means if we add these three numbers together and divide by 3, we should get 897.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 897 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 897 * 3 = x + y + z
- So, the sum of our three numbers should be: 2691
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2691.
Solution 1:
897, 897, 897
Verification:
(897 + 897 + 897) / 3 = 2691 / 3 ≈ 897
This solution is correct!
Solution 2:
897, 897, 897
Verification:
(897 + 897 + 897) / 3 = 2691 / 3 ≈ 897
This solution is correct!
Solution 3:
1734, 199, 758
Verification:
(1734 + 199 + 758) / 3 = 2691 / 3 ≈ 897
This solution is correct!
Solution 4:
1794, 708, 189
Verification:
(1794 + 708 + 189) / 3 = 2691 / 3 ≈ 897
This solution is correct!
Solution 5:
1498, 170, 1023
Verification:
(1498 + 170 + 1023) / 3 = 2691 / 3 ≈ 897
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 2691 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.