What three numbers have an average of 577?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 577. This means if we add these three numbers together and divide by 3, we should get 577.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 577 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 577 * 3 = x + y + z
- So, the sum of our three numbers should be: 1731
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1731.
Solution 1:
577, 577, 577
Verification:
(577 + 577 + 577) / 3 = 1731 / 3 ≈ 577
This solution is correct!
Solution 2:
577, 577, 577
Verification:
(577 + 577 + 577) / 3 = 1731 / 3 ≈ 577
This solution is correct!
Solution 3:
739, 293, 699
Verification:
(739 + 293 + 699) / 3 = 1731 / 3 ≈ 577
This solution is correct!
Solution 4:
1464, 163, 104
Verification:
(1464 + 163 + 104) / 3 = 1731 / 3 ≈ 577
This solution is correct!
Solution 5:
1497, 173, 61
Verification:
(1497 + 173 + 61) / 3 = 1731 / 3 ≈ 577
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 1731 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.