What three numbers have an average of 125?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 125. This means if we add these three numbers together and divide by 3, we should get 125.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 125 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 125 * 3 = x + y + z
- So, the sum of our three numbers should be: 375
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 375.
Solution 1:
125, 125, 125
Verification:
(125 + 125 + 125) / 3 = 375 / 3 ≈ 125
This solution is correct!
Solution 2:
125, 125, 125
Verification:
(125 + 125 + 125) / 3 = 375 / 3 ≈ 125
This solution is correct!
Solution 3:
102, 181, 92
Verification:
(102 + 181 + 92) / 3 = 375 / 3 ≈ 125
This solution is correct!
Solution 4:
11, 254, 110
Verification:
(11 + 254 + 110) / 3 = 375 / 3 ≈ 125
This solution is correct!
Solution 5:
91, 2, 282
Verification:
(91 + 2 + 282) / 3 = 375 / 3 ≈ 125
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 375 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.