What three numbers have an average of 957?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 957. This means if we add these three numbers together and divide by 3, we should get 957.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 957 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 957 * 3 = x + y + z
- So, the sum of our three numbers should be: 2871
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2871.
Solution 1:
957, 957, 957
Verification:
(957 + 957 + 957) / 3 = 2871 / 3 ≈ 957
This solution is correct!
Solution 2:
957, 957, 957
Verification:
(957 + 957 + 957) / 3 = 2871 / 3 ≈ 957
This solution is correct!
Solution 3:
544, 984, 1343
Verification:
(544 + 984 + 1343) / 3 = 2871 / 3 ≈ 957
This solution is correct!
Solution 4:
371, 2198, 302
Verification:
(371 + 2198 + 302) / 3 = 2871 / 3 ≈ 957
This solution is correct!
Solution 5:
2297, 387, 187
Verification:
(2297 + 387 + 187) / 3 = 2871 / 3 ≈ 957
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 2871 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.