What three numbers have an average of 871?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 871. This means if we add these three numbers together and divide by 3, we should get 871.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 871 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 871 * 3 = x + y + z
- So, the sum of our three numbers should be: 2613
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2613.
Solution 1:
871, 871, 871
Verification:
(871 + 871 + 871) / 3 = 2613 / 3 ≈ 871
This solution is correct!
Solution 2:
871, 871, 871
Verification:
(871 + 871 + 871) / 3 = 2613 / 3 ≈ 871
This solution is correct!
Solution 3:
913, 88, 1612
Verification:
(913 + 88 + 1612) / 3 = 2613 / 3 ≈ 871
This solution is correct!
Solution 4:
164, 2257, 192
Verification:
(164 + 2257 + 192) / 3 = 2613 / 3 ≈ 871
This solution is correct!
Solution 5:
1521, 334, 758
Verification:
(1521 + 334 + 758) / 3 = 2613 / 3 ≈ 871
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 2613 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.