What three numbers have an average of 274?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 274. This means if we add these three numbers together and divide by 3, we should get 274.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 274 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 274 * 3 = x + y + z
- So, the sum of our three numbers should be: 822
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 822.
Solution 1:
274, 274, 274
Verification:
(274 + 274 + 274) / 3 = 822 / 3 ≈ 274
This solution is correct!
Solution 2:
274, 274, 274
Verification:
(274 + 274 + 274) / 3 = 822 / 3 ≈ 274
This solution is correct!
Solution 3:
200, 535, 87
Verification:
(200 + 535 + 87) / 3 = 822 / 3 ≈ 274
This solution is correct!
Solution 4:
276, 118, 428
Verification:
(276 + 118 + 428) / 3 = 822 / 3 ≈ 274
This solution is correct!
Solution 5:
646, 67, 109
Verification:
(646 + 67 + 109) / 3 = 822 / 3 ≈ 274
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 822 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.