What three numbers have an average of 25?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 25. This means if we add these three numbers together and divide by 3, we should get 25.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 25 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 25 * 3 = x + y + z
- So, the sum of our three numbers should be: 75
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 75.
Solution 1:
25, 25, 25
Verification:
(25 + 25 + 25) / 3 = 75 / 3 ≈ 25
This solution is correct!
Solution 2:
25, 25, 25
Verification:
(25 + 25 + 25) / 3 = 75 / 3 ≈ 25
This solution is correct!
Solution 3:
57, 12, 6
Verification:
(57 + 12 + 6) / 3 = 75 / 3 ≈ 25
This solution is correct!
Solution 4:
53, 2, 20
Verification:
(53 + 2 + 20) / 3 = 75 / 3 ≈ 25
This solution is correct!
Solution 5:
3, 66, 6
Verification:
(3 + 66 + 6) / 3 = 75 / 3 ≈ 25
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 75 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.