What three numbers have an average of 276?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 276. This means if we add these three numbers together and divide by 3, we should get 276.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 276 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 276 * 3 = x + y + z
- So, the sum of our three numbers should be: 828
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 828.
Solution 1:
276, 276, 276
Verification:
(276 + 276 + 276) / 3 = 828 / 3 ≈ 276
This solution is correct!
Solution 2:
276, 276, 276
Verification:
(276 + 276 + 276) / 3 = 828 / 3 ≈ 276
This solution is correct!
Solution 3:
498, 52, 278
Verification:
(498 + 52 + 278) / 3 = 828 / 3 ≈ 276
This solution is correct!
Solution 4:
797, 15, 16
Verification:
(797 + 15 + 16) / 3 = 828 / 3 ≈ 276
This solution is correct!
Solution 5:
596, 204, 28
Verification:
(596 + 204 + 28) / 3 = 828 / 3 ≈ 276
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 828 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.