What three numbers have an average of 917?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 917. This means if we add these three numbers together and divide by 3, we should get 917.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 917 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 917 * 3 = x + y + z
- So, the sum of our three numbers should be: 2751
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2751.
Solution 1:
917, 917, 917
Verification:
(917 + 917 + 917) / 3 = 2751 / 3 ≈ 917
This solution is correct!
Solution 2:
917, 917, 917
Verification:
(917 + 917 + 917) / 3 = 2751 / 3 ≈ 917
This solution is correct!
Solution 3:
1511, 914, 326
Verification:
(1511 + 914 + 326) / 3 = 2751 / 3 ≈ 917
This solution is correct!
Solution 4:
970, 1739, 42
Verification:
(970 + 1739 + 42) / 3 = 2751 / 3 ≈ 917
This solution is correct!
Solution 5:
1103, 736, 912
Verification:
(1103 + 736 + 912) / 3 = 2751 / 3 ≈ 917
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 2751 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.