What three numbers have an average of 611?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 611. This means if we add these three numbers together and divide by 3, we should get 611.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 611 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 611 * 3 = x + y + z
- So, the sum of our three numbers should be: 1833
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1833.
Solution 1:
611, 611, 611
Verification:
(611 + 611 + 611) / 3 = 1833 / 3 ≈ 611
This solution is correct!
Solution 2:
611, 611, 611
Verification:
(611 + 611 + 611) / 3 = 1833 / 3 ≈ 611
This solution is correct!
Solution 3:
1571, 178, 84
Verification:
(1571 + 178 + 84) / 3 = 1833 / 3 ≈ 611
This solution is correct!
Solution 4:
1281, 543, 9
Verification:
(1281 + 543 + 9) / 3 = 1833 / 3 ≈ 611
This solution is correct!
Solution 5:
1764, 51, 18
Verification:
(1764 + 51 + 18) / 3 = 1833 / 3 ≈ 611
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 1833 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.