What three numbers have an average of 983?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 983. This means if we add these three numbers together and divide by 3, we should get 983.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 983 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 983 * 3 = x + y + z
- So, the sum of our three numbers should be: 2949
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2949.
Solution 1:
983, 983, 983
Verification:
(983 + 983 + 983) / 3 = 2949 / 3 ≈ 983
This solution is correct!
Solution 2:
983, 983, 983
Verification:
(983 + 983 + 983) / 3 = 2949 / 3 ≈ 983
This solution is correct!
Solution 3:
2415, 287, 247
Verification:
(2415 + 287 + 247) / 3 = 2949 / 3 ≈ 983
This solution is correct!
Solution 4:
2686, 164, 99
Verification:
(2686 + 164 + 99) / 3 = 2949 / 3 ≈ 983
This solution is correct!
Solution 5:
1147, 297, 1505
Verification:
(1147 + 297 + 1505) / 3 = 2949 / 3 ≈ 983
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 2949 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.