What three numbers have an average of 778?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 778. This means if we add these three numbers together and divide by 3, we should get 778.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 778 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 778 * 3 = x + y + z
- So, the sum of our three numbers should be: 2334
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2334.
Solution 1:
778, 778, 778
Verification:
(778 + 778 + 778) / 3 = 2334 / 3 ≈ 778
This solution is correct!
Solution 2:
778, 778, 778
Verification:
(778 + 778 + 778) / 3 = 2334 / 3 ≈ 778
This solution is correct!
Solution 3:
2067, 204, 63
Verification:
(2067 + 204 + 63) / 3 = 2334 / 3 ≈ 778
This solution is correct!
Solution 4:
330, 304, 1700
Verification:
(330 + 304 + 1700) / 3 = 2334 / 3 ≈ 778
This solution is correct!
Solution 5:
1176, 792, 366
Verification:
(1176 + 792 + 366) / 3 = 2334 / 3 ≈ 778
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 2334 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.