What three numbers have an average of 150?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 150. This means if we add these three numbers together and divide by 3, we should get 150.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 150 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 150 * 3 = x + y + z
- So, the sum of our three numbers should be: 450
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 450.
Solution 1:
150, 150, 150
Verification:
(150 + 150 + 150) / 3 = 450 / 3 ≈ 150
This solution is correct!
Solution 2:
150, 150, 150
Verification:
(150 + 150 + 150) / 3 = 450 / 3 ≈ 150
This solution is correct!
Solution 3:
139, 49, 262
Verification:
(139 + 49 + 262) / 3 = 450 / 3 ≈ 150
This solution is correct!
Solution 4:
352, 62, 36
Verification:
(352 + 62 + 36) / 3 = 450 / 3 ≈ 150
This solution is correct!
Solution 5:
58, 96, 296
Verification:
(58 + 96 + 296) / 3 = 450 / 3 ≈ 150
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 450 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.