What three numbers have an average of 48?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 48. This means if we add these three numbers together and divide by 3, we should get 48.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 48 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 48 * 3 = x + y + z
- So, the sum of our three numbers should be: 144
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 144.
Solution 1:
48, 48, 48
Verification:
(48 + 48 + 48) / 3 = 144 / 3 ≈ 48
This solution is correct!
Solution 2:
48, 48, 48
Verification:
(48 + 48 + 48) / 3 = 144 / 3 ≈ 48
This solution is correct!
Solution 3:
100, 12, 32
Verification:
(100 + 12 + 32) / 3 = 144 / 3 ≈ 48
This solution is correct!
Solution 4:
125, 17, 2
Verification:
(125 + 17 + 2) / 3 = 144 / 3 ≈ 48
This solution is correct!
Solution 5:
84, 32, 28
Verification:
(84 + 32 + 28) / 3 = 144 / 3 ≈ 48
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 144 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.