What three numbers have an average of 727?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 727. This means if we add these three numbers together and divide by 3, we should get 727.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 727 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 727 * 3 = x + y + z
- So, the sum of our three numbers should be: 2181
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2181.
Solution 1:
727, 727, 727
Verification:
(727 + 727 + 727) / 3 = 2181 / 3 ≈ 727
This solution is correct!
Solution 2:
727, 727, 727
Verification:
(727 + 727 + 727) / 3 = 2181 / 3 ≈ 727
This solution is correct!
Solution 3:
411, 136, 1634
Verification:
(411 + 136 + 1634) / 3 = 2181 / 3 ≈ 727
This solution is correct!
Solution 4:
1706, 130, 345
Verification:
(1706 + 130 + 345) / 3 = 2181 / 3 ≈ 727
This solution is correct!
Solution 5:
1131, 237, 813
Verification:
(1131 + 237 + 813) / 3 = 2181 / 3 ≈ 727
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 2181 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.