What three numbers have an average of 717?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 717. This means if we add these three numbers together and divide by 3, we should get 717.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 717 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 717 * 3 = x + y + z
- So, the sum of our three numbers should be: 2151
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2151.
Solution 1:
717, 717, 717
Verification:
(717 + 717 + 717) / 3 = 2151 / 3 ≈ 717
This solution is correct!
Solution 2:
717, 717, 717
Verification:
(717 + 717 + 717) / 3 = 2151 / 3 ≈ 717
This solution is correct!
Solution 3:
278, 686, 1187
Verification:
(278 + 686 + 1187) / 3 = 2151 / 3 ≈ 717
This solution is correct!
Solution 4:
1563, 518, 70
Verification:
(1563 + 518 + 70) / 3 = 2151 / 3 ≈ 717
This solution is correct!
Solution 5:
778, 1362, 11
Verification:
(778 + 1362 + 11) / 3 = 2151 / 3 ≈ 717
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 2151 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.