What three numbers have an average of 719?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 719. This means if we add these three numbers together and divide by 3, we should get 719.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 719 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 719 * 3 = x + y + z
- So, the sum of our three numbers should be: 2157
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2157.
Solution 1:
719, 719, 719
Verification:
(719 + 719 + 719) / 3 = 2157 / 3 ≈ 719
This solution is correct!
Solution 2:
719, 719, 719
Verification:
(719 + 719 + 719) / 3 = 2157 / 3 ≈ 719
This solution is correct!
Solution 3:
1506, 616, 35
Verification:
(1506 + 616 + 35) / 3 = 2157 / 3 ≈ 719
This solution is correct!
Solution 4:
1091, 961, 105
Verification:
(1091 + 961 + 105) / 3 = 2157 / 3 ≈ 719
This solution is correct!
Solution 5:
246, 1004, 907
Verification:
(246 + 1004 + 907) / 3 = 2157 / 3 ≈ 719
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 2157 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.