What three numbers have an average of 759?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 759. This means if we add these three numbers together and divide by 3, we should get 759.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 759 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 759 * 3 = x + y + z
- So, the sum of our three numbers should be: 2277
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2277.
Solution 1:
759, 759, 759
Verification:
(759 + 759 + 759) / 3 = 2277 / 3 ≈ 759
This solution is correct!
Solution 2:
759, 759, 759
Verification:
(759 + 759 + 759) / 3 = 2277 / 3 ≈ 759
This solution is correct!
Solution 3:
1267, 21, 989
Verification:
(1267 + 21 + 989) / 3 = 2277 / 3 ≈ 759
This solution is correct!
Solution 4:
224, 105, 1948
Verification:
(224 + 105 + 1948) / 3 = 2277 / 3 ≈ 759
This solution is correct!
Solution 5:
979, 1044, 254
Verification:
(979 + 1044 + 254) / 3 = 2277 / 3 ≈ 759
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 2277 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.