What three numbers have an average of 659?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 659. This means if we add these three numbers together and divide by 3, we should get 659.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 659 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 659 * 3 = x + y + z
- So, the sum of our three numbers should be: 1977
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1977.
Solution 1:
659, 659, 659
Verification:
(659 + 659 + 659) / 3 = 1977 / 3 ≈ 659
This solution is correct!
Solution 2:
659, 659, 659
Verification:
(659 + 659 + 659) / 3 = 1977 / 3 ≈ 659
This solution is correct!
Solution 3:
1077, 783, 117
Verification:
(1077 + 783 + 117) / 3 = 1977 / 3 ≈ 659
This solution is correct!
Solution 4:
1410, 483, 84
Verification:
(1410 + 483 + 84) / 3 = 1977 / 3 ≈ 659
This solution is correct!
Solution 5:
1305, 116, 556
Verification:
(1305 + 116 + 556) / 3 = 1977 / 3 ≈ 659
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 1977 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.