What three numbers have an average of 969?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 969. This means if we add these three numbers together and divide by 3, we should get 969.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 969 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 969 * 3 = x + y + z
- So, the sum of our three numbers should be: 2907
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2907.
Solution 1:
969, 969, 969
Verification:
(969 + 969 + 969) / 3 = 2907 / 3 ≈ 969
This solution is correct!
Solution 2:
969, 969, 969
Verification:
(969 + 969 + 969) / 3 = 2907 / 3 ≈ 969
This solution is correct!
Solution 3:
306, 2009, 592
Verification:
(306 + 2009 + 592) / 3 = 2907 / 3 ≈ 969
This solution is correct!
Solution 4:
387, 1341, 1179
Verification:
(387 + 1341 + 1179) / 3 = 2907 / 3 ≈ 969
This solution is correct!
Solution 5:
661, 349, 1897
Verification:
(661 + 349 + 1897) / 3 = 2907 / 3 ≈ 969
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 2907 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.