What three numbers have an average of 982?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 982. This means if we add these three numbers together and divide by 3, we should get 982.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 982 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 982 * 3 = x + y + z
- So, the sum of our three numbers should be: 2946
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2946.
Solution 1:
982, 982, 982
Verification:
(982 + 982 + 982) / 3 = 2946 / 3 ≈ 982
This solution is correct!
Solution 2:
982, 982, 982
Verification:
(982 + 982 + 982) / 3 = 2946 / 3 ≈ 982
This solution is correct!
Solution 3:
2051, 322, 573
Verification:
(2051 + 322 + 573) / 3 = 2946 / 3 ≈ 982
This solution is correct!
Solution 4:
206, 1889, 851
Verification:
(206 + 1889 + 851) / 3 = 2946 / 3 ≈ 982
This solution is correct!
Solution 5:
2061, 440, 445
Verification:
(2061 + 440 + 445) / 3 = 2946 / 3 ≈ 982
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 2946 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.