What three numbers have an average of 272?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 272. This means if we add these three numbers together and divide by 3, we should get 272.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 272 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 272 * 3 = x + y + z
- So, the sum of our three numbers should be: 816
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 816.
Solution 1:
272, 272, 272
Verification:
(272 + 272 + 272) / 3 = 816 / 3 ≈ 272
This solution is correct!
Solution 2:
272, 272, 272
Verification:
(272 + 272 + 272) / 3 = 816 / 3 ≈ 272
This solution is correct!
Solution 3:
494, 123, 199
Verification:
(494 + 123 + 199) / 3 = 816 / 3 ≈ 272
This solution is correct!
Solution 4:
792, 23, 1
Verification:
(792 + 23 + 1) / 3 = 816 / 3 ≈ 272
This solution is correct!
Solution 5:
194, 376, 246
Verification:
(194 + 376 + 246) / 3 = 816 / 3 ≈ 272
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 816 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.