What three numbers have an average of 984?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 984. This means if we add these three numbers together and divide by 3, we should get 984.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 984 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 984 * 3 = x + y + z
- So, the sum of our three numbers should be: 2952
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2952.
Solution 1:
984, 984, 984
Verification:
(984 + 984 + 984) / 3 = 2952 / 3 ≈ 984
This solution is correct!
Solution 2:
984, 984, 984
Verification:
(984 + 984 + 984) / 3 = 2952 / 3 ≈ 984
This solution is correct!
Solution 3:
853, 1237, 862
Verification:
(853 + 1237 + 862) / 3 = 2952 / 3 ≈ 984
This solution is correct!
Solution 4:
1904, 965, 83
Verification:
(1904 + 965 + 83) / 3 = 2952 / 3 ≈ 984
This solution is correct!
Solution 5:
1191, 666, 1095
Verification:
(1191 + 666 + 1095) / 3 = 2952 / 3 ≈ 984
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 2952 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.