What three numbers have an average of 275?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 275. This means if we add these three numbers together and divide by 3, we should get 275.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 275 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 275 * 3 = x + y + z
- So, the sum of our three numbers should be: 825
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 825.
Solution 1:
275, 275, 275
Verification:
(275 + 275 + 275) / 3 = 825 / 3 ≈ 275
This solution is correct!
Solution 2:
275, 275, 275
Verification:
(275 + 275 + 275) / 3 = 825 / 3 ≈ 275
This solution is correct!
Solution 3:
298, 494, 33
Verification:
(298 + 494 + 33) / 3 = 825 / 3 ≈ 275
This solution is correct!
Solution 4:
641, 149, 35
Verification:
(641 + 149 + 35) / 3 = 825 / 3 ≈ 275
This solution is correct!
Solution 5:
104, 615, 106
Verification:
(104 + 615 + 106) / 3 = 825 / 3 ≈ 275
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 825 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.