What three numbers have an average of 750?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 750. This means if we add these three numbers together and divide by 3, we should get 750.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 750 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 750 * 3 = x + y + z
- So, the sum of our three numbers should be: 2250
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2250.
Solution 1:
750, 750, 750
Verification:
(750 + 750 + 750) / 3 = 2250 / 3 ≈ 750
This solution is correct!
Solution 2:
750, 750, 750
Verification:
(750 + 750 + 750) / 3 = 2250 / 3 ≈ 750
This solution is correct!
Solution 3:
850, 526, 874
Verification:
(850 + 526 + 874) / 3 = 2250 / 3 ≈ 750
This solution is correct!
Solution 4:
1514, 90, 646
Verification:
(1514 + 90 + 646) / 3 = 2250 / 3 ≈ 750
This solution is correct!
Solution 5:
820, 229, 1201
Verification:
(820 + 229 + 1201) / 3 = 2250 / 3 ≈ 750
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 2250 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.