What three numbers have an average of 766?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 766. This means if we add these three numbers together and divide by 3, we should get 766.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 766 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 766 * 3 = x + y + z
- So, the sum of our three numbers should be: 2298
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2298.
Solution 1:
766, 766, 766
Verification:
(766 + 766 + 766) / 3 = 2298 / 3 ≈ 766
This solution is correct!
Solution 2:
766, 766, 766
Verification:
(766 + 766 + 766) / 3 = 2298 / 3 ≈ 766
This solution is correct!
Solution 3:
188, 1891, 219
Verification:
(188 + 1891 + 219) / 3 = 2298 / 3 ≈ 766
This solution is correct!
Solution 4:
213, 344, 1741
Verification:
(213 + 344 + 1741) / 3 = 2298 / 3 ≈ 766
This solution is correct!
Solution 5:
1172, 335, 791
Verification:
(1172 + 335 + 791) / 3 = 2298 / 3 ≈ 766
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 2298 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.