What three numbers have an average of 981?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 981. This means if we add these three numbers together and divide by 3, we should get 981.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 981 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 981 * 3 = x + y + z
- So, the sum of our three numbers should be: 2943
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2943.
Solution 1:
981, 981, 981
Verification:
(981 + 981 + 981) / 3 = 2943 / 3 ≈ 981
This solution is correct!
Solution 2:
981, 981, 981
Verification:
(981 + 981 + 981) / 3 = 2943 / 3 ≈ 981
This solution is correct!
Solution 3:
1384, 1090, 469
Verification:
(1384 + 1090 + 469) / 3 = 2943 / 3 ≈ 981
This solution is correct!
Solution 4:
1595, 599, 749
Verification:
(1595 + 599 + 749) / 3 = 2943 / 3 ≈ 981
This solution is correct!
Solution 5:
2871, 6, 66
Verification:
(2871 + 6 + 66) / 3 = 2943 / 3 ≈ 981
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 2943 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.