What three numbers have an average of 896?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 896. This means if we add these three numbers together and divide by 3, we should get 896.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 896 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 896 * 3 = x + y + z
- So, the sum of our three numbers should be: 2688
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2688.
Solution 1:
896, 896, 896
Verification:
(896 + 896 + 896) / 3 = 2688 / 3 ≈ 896
This solution is correct!
Solution 2:
896, 896, 896
Verification:
(896 + 896 + 896) / 3 = 2688 / 3 ≈ 896
This solution is correct!
Solution 3:
5, 980, 1703
Verification:
(5 + 980 + 1703) / 3 = 2688 / 3 ≈ 896
This solution is correct!
Solution 4:
5, 2438, 245
Verification:
(5 + 2438 + 245) / 3 = 2688 / 3 ≈ 896
This solution is correct!
Solution 5:
1326, 371, 991
Verification:
(1326 + 371 + 991) / 3 = 2688 / 3 ≈ 896
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 2688 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.