What three numbers have an average of 905?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 905. This means if we add these three numbers together and divide by 3, we should get 905.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 905 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 905 * 3 = x + y + z
- So, the sum of our three numbers should be: 2715
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2715.
Solution 1:
905, 905, 905
Verification:
(905 + 905 + 905) / 3 = 2715 / 3 ≈ 905
This solution is correct!
Solution 2:
905, 905, 905
Verification:
(905 + 905 + 905) / 3 = 2715 / 3 ≈ 905
This solution is correct!
Solution 3:
474, 909, 1332
Verification:
(474 + 909 + 1332) / 3 = 2715 / 3 ≈ 905
This solution is correct!
Solution 4:
2030, 536, 149
Verification:
(2030 + 536 + 149) / 3 = 2715 / 3 ≈ 905
This solution is correct!
Solution 5:
1633, 265, 817
Verification:
(1633 + 265 + 817) / 3 = 2715 / 3 ≈ 905
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 2715 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.