What three numbers have an average of 247?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 247. This means if we add these three numbers together and divide by 3, we should get 247.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 247 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 247 * 3 = x + y + z
- So, the sum of our three numbers should be: 741
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 741.
Solution 1:
247, 247, 247
Verification:
(247 + 247 + 247) / 3 = 741 / 3 ≈ 247
This solution is correct!
Solution 2:
247, 247, 247
Verification:
(247 + 247 + 247) / 3 = 741 / 3 ≈ 247
This solution is correct!
Solution 3:
650, 67, 24
Verification:
(650 + 67 + 24) / 3 = 741 / 3 ≈ 247
This solution is correct!
Solution 4:
540, 176, 25
Verification:
(540 + 176 + 25) / 3 = 741 / 3 ≈ 247
This solution is correct!
Solution 5:
307, 70, 364
Verification:
(307 + 70 + 364) / 3 = 741 / 3 ≈ 247
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 741 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.