What three numbers have an average of 679?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 679. This means if we add these three numbers together and divide by 3, we should get 679.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 679 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 679 * 3 = x + y + z
- So, the sum of our three numbers should be: 2037
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2037.
Solution 1:
679, 679, 679
Verification:
(679 + 679 + 679) / 3 = 2037 / 3 ≈ 679
This solution is correct!
Solution 2:
679, 679, 679
Verification:
(679 + 679 + 679) / 3 = 2037 / 3 ≈ 679
This solution is correct!
Solution 3:
1017, 265, 755
Verification:
(1017 + 265 + 755) / 3 = 2037 / 3 ≈ 679
This solution is correct!
Solution 4:
771, 793, 473
Verification:
(771 + 793 + 473) / 3 = 2037 / 3 ≈ 679
This solution is correct!
Solution 5:
1031, 135, 871
Verification:
(1031 + 135 + 871) / 3 = 2037 / 3 ≈ 679
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 2037 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.