What three numbers have an average of 19?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 19. This means if we add these three numbers together and divide by 3, we should get 19.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 19 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 19 * 3 = x + y + z
- So, the sum of our three numbers should be: 57
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 57.
Solution 1:
19, 19, 19
Verification:
(19 + 19 + 19) / 3 = 57 / 3 ≈ 19
This solution is correct!
Solution 2:
19, 19, 19
Verification:
(19 + 19 + 19) / 3 = 57 / 3 ≈ 19
This solution is correct!
Solution 3:
49, 7, 1
Verification:
(49 + 7 + 1) / 3 = 57 / 3 ≈ 19
This solution is correct!
Solution 4:
32, 2, 23
Verification:
(32 + 2 + 23) / 3 = 57 / 3 ≈ 19
This solution is correct!
Solution 5:
52, 3, 2
Verification:
(52 + 3 + 2) / 3 = 57 / 3 ≈ 19
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 57 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.