What three numbers have an average of 661?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 661. This means if we add these three numbers together and divide by 3, we should get 661.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 661 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 661 * 3 = x + y + z
- So, the sum of our three numbers should be: 1983
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1983.
Solution 1:
661, 661, 661
Verification:
(661 + 661 + 661) / 3 = 1983 / 3 ≈ 661
This solution is correct!
Solution 2:
661, 661, 661
Verification:
(661 + 661 + 661) / 3 = 1983 / 3 ≈ 661
This solution is correct!
Solution 3:
1529, 217, 237
Verification:
(1529 + 217 + 237) / 3 = 1983 / 3 ≈ 661
This solution is correct!
Solution 4:
210, 1124, 649
Verification:
(210 + 1124 + 649) / 3 = 1983 / 3 ≈ 661
This solution is correct!
Solution 5:
148, 77, 1758
Verification:
(148 + 77 + 1758) / 3 = 1983 / 3 ≈ 661
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 1983 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.