What three numbers have an average of 968?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 968. This means if we add these three numbers together and divide by 3, we should get 968.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 968 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 968 * 3 = x + y + z
- So, the sum of our three numbers should be: 2904
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2904.
Solution 1:
968, 968, 968
Verification:
(968 + 968 + 968) / 3 = 2904 / 3 ≈ 968
This solution is correct!
Solution 2:
968, 968, 968
Verification:
(968 + 968 + 968) / 3 = 2904 / 3 ≈ 968
This solution is correct!
Solution 3:
1377, 583, 944
Verification:
(1377 + 583 + 944) / 3 = 2904 / 3 ≈ 968
This solution is correct!
Solution 4:
1822, 922, 160
Verification:
(1822 + 922 + 160) / 3 = 2904 / 3 ≈ 968
This solution is correct!
Solution 5:
2581, 140, 183
Verification:
(2581 + 140 + 183) / 3 = 2904 / 3 ≈ 968
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 2904 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.