What three numbers have an average of 898?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 898. This means if we add these three numbers together and divide by 3, we should get 898.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 898 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 898 * 3 = x + y + z
- So, the sum of our three numbers should be: 2694
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2694.
Solution 1:
898, 898, 898
Verification:
(898 + 898 + 898) / 3 = 2694 / 3 ≈ 898
This solution is correct!
Solution 2:
898, 898, 898
Verification:
(898 + 898 + 898) / 3 = 2694 / 3 ≈ 898
This solution is correct!
Solution 3:
1629, 295, 770
Verification:
(1629 + 295 + 770) / 3 = 2694 / 3 ≈ 898
This solution is correct!
Solution 4:
143, 1536, 1015
Verification:
(143 + 1536 + 1015) / 3 = 2694 / 3 ≈ 898
This solution is correct!
Solution 5:
2461, 92, 141
Verification:
(2461 + 92 + 141) / 3 = 2694 / 3 ≈ 898
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 2694 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.