What three numbers have an average of 762?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 762. This means if we add these three numbers together and divide by 3, we should get 762.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 762 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 762 * 3 = x + y + z
- So, the sum of our three numbers should be: 2286
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2286.
Solution 1:
762, 762, 762
Verification:
(762 + 762 + 762) / 3 = 2286 / 3 ≈ 762
This solution is correct!
Solution 2:
762, 762, 762
Verification:
(762 + 762 + 762) / 3 = 2286 / 3 ≈ 762
This solution is correct!
Solution 3:
988, 834, 464
Verification:
(988 + 834 + 464) / 3 = 2286 / 3 ≈ 762
This solution is correct!
Solution 4:
377, 1793, 116
Verification:
(377 + 1793 + 116) / 3 = 2286 / 3 ≈ 762
This solution is correct!
Solution 5:
68, 404, 1814
Verification:
(68 + 404 + 1814) / 3 = 2286 / 3 ≈ 762
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 2286 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.