What three numbers have an average of 774?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 774. This means if we add these three numbers together and divide by 3, we should get 774.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 774 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 774 * 3 = x + y + z
- So, the sum of our three numbers should be: 2322
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2322.
Solution 1:
774, 774, 774
Verification:
(774 + 774 + 774) / 3 = 2322 / 3 ≈ 774
This solution is correct!
Solution 2:
774, 774, 774
Verification:
(774 + 774 + 774) / 3 = 2322 / 3 ≈ 774
This solution is correct!
Solution 3:
983, 566, 773
Verification:
(983 + 566 + 773) / 3 = 2322 / 3 ≈ 774
This solution is correct!
Solution 4:
1116, 972, 234
Verification:
(1116 + 972 + 234) / 3 = 2322 / 3 ≈ 774
This solution is correct!
Solution 5:
105, 1796, 421
Verification:
(105 + 1796 + 421) / 3 = 2322 / 3 ≈ 774
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 2322 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.