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:
1362, 390, 225
Verification:
(1362 + 390 + 225) / 3 = 1977 / 3 ≈ 659
This solution is correct!
Solution 4:
1518, 77, 382
Verification:
(1518 + 77 + 382) / 3 = 1977 / 3 ≈ 659
This solution is correct!
Solution 5:
334, 285, 1358
Verification:
(334 + 285 + 1358) / 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.