What three numbers have an average of 660?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 660. This means if we add these three numbers together and divide by 3, we should get 660.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 660 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 660 * 3 = x + y + z
- So, the sum of our three numbers should be: 1980
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1980.
Solution 1:
660, 660, 660
Verification:
(660 + 660 + 660) / 3 = 1980 / 3 ≈ 660
This solution is correct!
Solution 2:
660, 660, 660
Verification:
(660 + 660 + 660) / 3 = 1980 / 3 ≈ 660
This solution is correct!
Solution 3:
1129, 501, 350
Verification:
(1129 + 501 + 350) / 3 = 1980 / 3 ≈ 660
This solution is correct!
Solution 4:
835, 738, 407
Verification:
(835 + 738 + 407) / 3 = 1980 / 3 ≈ 660
This solution is correct!
Solution 5:
264, 9, 1707
Verification:
(264 + 9 + 1707) / 3 = 1980 / 3 ≈ 660
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 1980 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.