What three numbers have an average of 277?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 277. This means if we add these three numbers together and divide by 3, we should get 277.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 277 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 277 * 3 = x + y + z
- So, the sum of our three numbers should be: 831
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 831.
Solution 1:
277, 277, 277
Verification:
(277 + 277 + 277) / 3 = 831 / 3 ≈ 277
This solution is correct!
Solution 2:
277, 277, 277
Verification:
(277 + 277 + 277) / 3 = 831 / 3 ≈ 277
This solution is correct!
Solution 3:
96, 272, 463
Verification:
(96 + 272 + 463) / 3 = 831 / 3 ≈ 277
This solution is correct!
Solution 4:
686, 47, 98
Verification:
(686 + 47 + 98) / 3 = 831 / 3 ≈ 277
This solution is correct!
Solution 5:
161, 490, 180
Verification:
(161 + 490 + 180) / 3 = 831 / 3 ≈ 277
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 831 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.