What three numbers have an average of 976?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 976. This means if we add these three numbers together and divide by 3, we should get 976.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 976 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 976 * 3 = x + y + z
- So, the sum of our three numbers should be: 2928
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2928.
Solution 1:
976, 976, 976
Verification:
(976 + 976 + 976) / 3 = 2928 / 3 ≈ 976
This solution is correct!
Solution 2:
976, 976, 976
Verification:
(976 + 976 + 976) / 3 = 2928 / 3 ≈ 976
This solution is correct!
Solution 3:
2605, 268, 55
Verification:
(2605 + 268 + 55) / 3 = 2928 / 3 ≈ 976
This solution is correct!
Solution 4:
756, 2083, 89
Verification:
(756 + 2083 + 89) / 3 = 2928 / 3 ≈ 976
This solution is correct!
Solution 5:
2859, 50, 19
Verification:
(2859 + 50 + 19) / 3 = 2928 / 3 ≈ 976
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 2928 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.