What three numbers have an average of 748?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 748. This means if we add these three numbers together and divide by 3, we should get 748.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 748 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 748 * 3 = x + y + z
- So, the sum of our three numbers should be: 2244
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2244.
Solution 1:
748, 748, 748
Verification:
(748 + 748 + 748) / 3 = 2244 / 3 ≈ 748
This solution is correct!
Solution 2:
748, 748, 748
Verification:
(748 + 748 + 748) / 3 = 2244 / 3 ≈ 748
This solution is correct!
Solution 3:
1838, 233, 173
Verification:
(1838 + 233 + 173) / 3 = 2244 / 3 ≈ 748
This solution is correct!
Solution 4:
842, 1157, 245
Verification:
(842 + 1157 + 245) / 3 = 2244 / 3 ≈ 748
This solution is correct!
Solution 5:
1442, 186, 616
Verification:
(1442 + 186 + 616) / 3 = 2244 / 3 ≈ 748
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 2244 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.