What three numbers have an average of 783?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 783. This means if we add these three numbers together and divide by 3, we should get 783.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 783 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 783 * 3 = x + y + z
- So, the sum of our three numbers should be: 2349
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2349.
Solution 1:
783, 783, 783
Verification:
(783 + 783 + 783) / 3 = 2349 / 3 ≈ 783
This solution is correct!
Solution 2:
783, 783, 783
Verification:
(783 + 783 + 783) / 3 = 2349 / 3 ≈ 783
This solution is correct!
Solution 3:
1763, 455, 131
Verification:
(1763 + 455 + 131) / 3 = 2349 / 3 ≈ 783
This solution is correct!
Solution 4:
1595, 69, 685
Verification:
(1595 + 69 + 685) / 3 = 2349 / 3 ≈ 783
This solution is correct!
Solution 5:
749, 321, 1279
Verification:
(749 + 321 + 1279) / 3 = 2349 / 3 ≈ 783
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 2349 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.