What three numbers have an average of 144?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 144. This means if we add these three numbers together and divide by 3, we should get 144.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 144 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 144 * 3 = x + y + z
- So, the sum of our three numbers should be: 432
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 432.
Solution 1:
144, 144, 144
Verification:
(144 + 144 + 144) / 3 = 432 / 3 ≈ 144
This solution is correct!
Solution 2:
144, 144, 144
Verification:
(144 + 144 + 144) / 3 = 432 / 3 ≈ 144
This solution is correct!
Solution 3:
14, 345, 73
Verification:
(14 + 345 + 73) / 3 = 432 / 3 ≈ 144
This solution is correct!
Solution 4:
233, 114, 85
Verification:
(233 + 114 + 85) / 3 = 432 / 3 ≈ 144
This solution is correct!
Solution 5:
106, 21, 305
Verification:
(106 + 21 + 305) / 3 = 432 / 3 ≈ 144
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 432 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.