What three numbers have an average of 763?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 763. This means if we add these three numbers together and divide by 3, we should get 763.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 763 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 763 * 3 = x + y + z
- So, the sum of our three numbers should be: 2289
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2289.
Solution 1:
763, 763, 763
Verification:
(763 + 763 + 763) / 3 = 2289 / 3 ≈ 763
This solution is correct!
Solution 2:
763, 763, 763
Verification:
(763 + 763 + 763) / 3 = 2289 / 3 ≈ 763
This solution is correct!
Solution 3:
842, 759, 688
Verification:
(842 + 759 + 688) / 3 = 2289 / 3 ≈ 763
This solution is correct!
Solution 4:
1676, 361, 252
Verification:
(1676 + 361 + 252) / 3 = 2289 / 3 ≈ 763
This solution is correct!
Solution 5:
666, 52, 1571
Verification:
(666 + 52 + 1571) / 3 = 2289 / 3 ≈ 763
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 2289 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.