What three numbers have an average of 248?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 248. This means if we add these three numbers together and divide by 3, we should get 248.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 248 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 248 * 3 = x + y + z
- So, the sum of our three numbers should be: 744
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 744.
Solution 1:
248, 248, 248
Verification:
(248 + 248 + 248) / 3 = 744 / 3 ≈ 248
This solution is correct!
Solution 2:
248, 248, 248
Verification:
(248 + 248 + 248) / 3 = 744 / 3 ≈ 248
This solution is correct!
Solution 3:
617, 37, 90
Verification:
(617 + 37 + 90) / 3 = 744 / 3 ≈ 248
This solution is correct!
Solution 4:
693, 34, 17
Verification:
(693 + 34 + 17) / 3 = 744 / 3 ≈ 248
This solution is correct!
Solution 5:
153, 437, 154
Verification:
(153 + 437 + 154) / 3 = 744 / 3 ≈ 248
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 744 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.