What three numbers have an average of 240?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 240. This means if we add these three numbers together and divide by 3, we should get 240.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 240 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 240 * 3 = x + y + z
- So, the sum of our three numbers should be: 720
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 720.
Solution 1:
240, 240, 240
Verification:
(240 + 240 + 240) / 3 = 720 / 3 ≈ 240
This solution is correct!
Solution 2:
240, 240, 240
Verification:
(240 + 240 + 240) / 3 = 720 / 3 ≈ 240
This solution is correct!
Solution 3:
543, 27, 150
Verification:
(543 + 27 + 150) / 3 = 720 / 3 ≈ 240
This solution is correct!
Solution 4:
469, 188, 63
Verification:
(469 + 188 + 63) / 3 = 720 / 3 ≈ 240
This solution is correct!
Solution 5:
318, 287, 115
Verification:
(318 + 287 + 115) / 3 = 720 / 3 ≈ 240
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 720 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.