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:
1769, 1144, 33
Verification:
(1769 + 1144 + 33) / 3 = 2946 / 3 ≈ 982
This solution is correct!
Solution 4:
2309, 129, 508
Verification:
(2309 + 129 + 508) / 3 = 2946 / 3 ≈ 982
This solution is correct!
Solution 5:
253, 951, 1742
Verification:
(253 + 951 + 1742) / 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.