What three numbers have an average of 705?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 705. This means if we add these three numbers together and divide by 3, we should get 705.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 705 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 705 * 3 = x + y + z
- So, the sum of our three numbers should be: 2115
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2115.
Solution 1:
705, 705, 705
Verification:
(705 + 705 + 705) / 3 = 2115 / 3 ≈ 705
This solution is correct!
Solution 2:
705, 705, 705
Verification:
(705 + 705 + 705) / 3 = 2115 / 3 ≈ 705
This solution is correct!
Solution 3:
1155, 68, 892
Verification:
(1155 + 68 + 892) / 3 = 2115 / 3 ≈ 705
This solution is correct!
Solution 4:
1271, 410, 434
Verification:
(1271 + 410 + 434) / 3 = 2115 / 3 ≈ 705
This solution is correct!
Solution 5:
600, 468, 1047
Verification:
(600 + 468 + 1047) / 3 = 2115 / 3 ≈ 705
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 2115 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.