What three numbers have an average of 694?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 694. This means if we add these three numbers together and divide by 3, we should get 694.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 694 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 694 * 3 = x + y + z
- So, the sum of our three numbers should be: 2082
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2082.
Solution 1:
694, 694, 694
Verification:
(694 + 694 + 694) / 3 = 2082 / 3 ≈ 694
This solution is correct!
Solution 2:
694, 694, 694
Verification:
(694 + 694 + 694) / 3 = 2082 / 3 ≈ 694
This solution is correct!
Solution 3:
960, 798, 324
Verification:
(960 + 798 + 324) / 3 = 2082 / 3 ≈ 694
This solution is correct!
Solution 4:
896, 523, 663
Verification:
(896 + 523 + 663) / 3 = 2082 / 3 ≈ 694
This solution is correct!
Solution 5:
669, 51, 1362
Verification:
(669 + 51 + 1362) / 3 = 2082 / 3 ≈ 694
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 2082 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.