What three numbers have an average of 776?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 776. This means if we add these three numbers together and divide by 3, we should get 776.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 776 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 776 * 3 = x + y + z
- So, the sum of our three numbers should be: 2328
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2328.
Solution 1:
776, 776, 776
Verification:
(776 + 776 + 776) / 3 = 2328 / 3 ≈ 776
This solution is correct!
Solution 2:
776, 776, 776
Verification:
(776 + 776 + 776) / 3 = 2328 / 3 ≈ 776
This solution is correct!
Solution 3:
1000, 1144, 184
Verification:
(1000 + 1144 + 184) / 3 = 2328 / 3 ≈ 776
This solution is correct!
Solution 4:
2283, 6, 39
Verification:
(2283 + 6 + 39) / 3 = 2328 / 3 ≈ 776
This solution is correct!
Solution 5:
1387, 823, 118
Verification:
(1387 + 823 + 118) / 3 = 2328 / 3 ≈ 776
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 2328 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.