What three numbers have an average of 154?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 154. This means if we add these three numbers together and divide by 3, we should get 154.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 154 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 154 * 3 = x + y + z
- So, the sum of our three numbers should be: 462
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 462.
Solution 1:
154, 154, 154
Verification:
(154 + 154 + 154) / 3 = 462 / 3 ≈ 154
This solution is correct!
Solution 2:
154, 154, 154
Verification:
(154 + 154 + 154) / 3 = 462 / 3 ≈ 154
This solution is correct!
Solution 3:
287, 107, 68
Verification:
(287 + 107 + 68) / 3 = 462 / 3 ≈ 154
This solution is correct!
Solution 4:
401, 58, 3
Verification:
(401 + 58 + 3) / 3 = 462 / 3 ≈ 154
This solution is correct!
Solution 5:
354, 92, 16
Verification:
(354 + 92 + 16) / 3 = 462 / 3 ≈ 154
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 462 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.