What three numbers have an average of 709?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 709. This means if we add these three numbers together and divide by 3, we should get 709.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 709 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 709 * 3 = x + y + z
- So, the sum of our three numbers should be: 2127
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2127.
Solution 1:
709, 709, 709
Verification:
(709 + 709 + 709) / 3 = 2127 / 3 ≈ 709
This solution is correct!
Solution 2:
709, 709, 709
Verification:
(709 + 709 + 709) / 3 = 2127 / 3 ≈ 709
This solution is correct!
Solution 3:
1887, 154, 86
Verification:
(1887 + 154 + 86) / 3 = 2127 / 3 ≈ 709
This solution is correct!
Solution 4:
2046, 28, 53
Verification:
(2046 + 28 + 53) / 3 = 2127 / 3 ≈ 709
This solution is correct!
Solution 5:
1416, 679, 32
Verification:
(1416 + 679 + 32) / 3 = 2127 / 3 ≈ 709
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 2127 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.