What three numbers have an average of 297?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 297. This means if we add these three numbers together and divide by 3, we should get 297.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 297 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 297 * 3 = x + y + z
- So, the sum of our three numbers should be: 891
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 891.
Solution 1:
297, 297, 297
Verification:
(297 + 297 + 297) / 3 = 891 / 3 ≈ 297
This solution is correct!
Solution 2:
297, 297, 297
Verification:
(297 + 297 + 297) / 3 = 891 / 3 ≈ 297
This solution is correct!
Solution 3:
48, 168, 675
Verification:
(48 + 168 + 675) / 3 = 891 / 3 ≈ 297
This solution is correct!
Solution 4:
573, 300, 18
Verification:
(573 + 300 + 18) / 3 = 891 / 3 ≈ 297
This solution is correct!
Solution 5:
44, 694, 153
Verification:
(44 + 694 + 153) / 3 = 891 / 3 ≈ 297
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 891 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.