What three numbers have an average of 751?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 751. This means if we add these three numbers together and divide by 3, we should get 751.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 751 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 751 * 3 = x + y + z
- So, the sum of our three numbers should be: 2253
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2253.
Solution 1:
751, 751, 751
Verification:
(751 + 751 + 751) / 3 = 2253 / 3 ≈ 751
This solution is correct!
Solution 2:
751, 751, 751
Verification:
(751 + 751 + 751) / 3 = 2253 / 3 ≈ 751
This solution is correct!
Solution 3:
1921, 190, 142
Verification:
(1921 + 190 + 142) / 3 = 2253 / 3 ≈ 751
This solution is correct!
Solution 4:
375, 1418, 460
Verification:
(375 + 1418 + 460) / 3 = 2253 / 3 ≈ 751
This solution is correct!
Solution 5:
157, 643, 1453
Verification:
(157 + 643 + 1453) / 3 = 2253 / 3 ≈ 751
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 2253 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.