What three numbers have an average of 148?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 148. This means if we add these three numbers together and divide by 3, we should get 148.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 148 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 148 * 3 = x + y + z
- So, the sum of our three numbers should be: 444
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 444.
Solution 1:
148, 148, 148
Verification:
(148 + 148 + 148) / 3 = 444 / 3 ≈ 148
This solution is correct!
Solution 2:
148, 148, 148
Verification:
(148 + 148 + 148) / 3 = 444 / 3 ≈ 148
This solution is correct!
Solution 3:
442, 1, 1
Verification:
(442 + 1 + 1) / 3 = 444 / 3 ≈ 148
This solution is correct!
Solution 4:
108, 298, 38
Verification:
(108 + 298 + 38) / 3 = 444 / 3 ≈ 148
This solution is correct!
Solution 5:
307, 38, 99
Verification:
(307 + 38 + 99) / 3 = 444 / 3 ≈ 148
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 444 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.