What three numbers have an average of 635?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 635. This means if we add these three numbers together and divide by 3, we should get 635.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 635 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 635 * 3 = x + y + z
- So, the sum of our three numbers should be: 1905
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1905.
Solution 1:
635, 635, 635
Verification:
(635 + 635 + 635) / 3 = 1905 / 3 ≈ 635
This solution is correct!
Solution 2:
635, 635, 635
Verification:
(635 + 635 + 635) / 3 = 1905 / 3 ≈ 635
This solution is correct!
Solution 3:
130, 749, 1026
Verification:
(130 + 749 + 1026) / 3 = 1905 / 3 ≈ 635
This solution is correct!
Solution 4:
1673, 38, 194
Verification:
(1673 + 38 + 194) / 3 = 1905 / 3 ≈ 635
This solution is correct!
Solution 5:
375, 594, 936
Verification:
(375 + 594 + 936) / 3 = 1905 / 3 ≈ 635
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 1905 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.