What three numbers have an average of 961?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 961. This means if we add these three numbers together and divide by 3, we should get 961.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 961 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 961 * 3 = x + y + z
- So, the sum of our three numbers should be: 2883
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2883.
Solution 1:
961, 961, 961
Verification:
(961 + 961 + 961) / 3 = 2883 / 3 ≈ 961
This solution is correct!
Solution 2:
961, 961, 961
Verification:
(961 + 961 + 961) / 3 = 2883 / 3 ≈ 961
This solution is correct!
Solution 3:
106, 1801, 976
Verification:
(106 + 1801 + 976) / 3 = 2883 / 3 ≈ 961
This solution is correct!
Solution 4:
142, 2520, 221
Verification:
(142 + 2520 + 221) / 3 = 2883 / 3 ≈ 961
This solution is correct!
Solution 5:
357, 2437, 89
Verification:
(357 + 2437 + 89) / 3 = 2883 / 3 ≈ 961
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 2883 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.