What three numbers have an average of 17?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 17. This means if we add these three numbers together and divide by 3, we should get 17.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 17 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 17 * 3 = x + y + z
- So, the sum of our three numbers should be: 51
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 51.
Solution 1:
17, 17, 17
Verification:
(17 + 17 + 17) / 3 = 51 / 3 ≈ 17
This solution is correct!
Solution 2:
17, 17, 17
Verification:
(17 + 17 + 17) / 3 = 51 / 3 ≈ 17
This solution is correct!
Solution 3:
36, 7, 8
Verification:
(36 + 7 + 8) / 3 = 51 / 3 ≈ 17
This solution is correct!
Solution 4:
3, 3, 45
Verification:
(3 + 3 + 45) / 3 = 51 / 3 ≈ 17
This solution is correct!
Solution 5:
46, 2, 3
Verification:
(46 + 2 + 3) / 3 = 51 / 3 ≈ 17
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 51 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.