What three numbers have an average of 675?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 675. This means if we add these three numbers together and divide by 3, we should get 675.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 675 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 675 * 3 = x + y + z
- So, the sum of our three numbers should be: 2025
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2025.
Solution 1:
675, 675, 675
Verification:
(675 + 675 + 675) / 3 = 2025 / 3 ≈ 675
This solution is correct!
Solution 2:
675, 675, 675
Verification:
(675 + 675 + 675) / 3 = 2025 / 3 ≈ 675
This solution is correct!
Solution 3:
781, 108, 1136
Verification:
(781 + 108 + 1136) / 3 = 2025 / 3 ≈ 675
This solution is correct!
Solution 4:
352, 1205, 468
Verification:
(352 + 1205 + 468) / 3 = 2025 / 3 ≈ 675
This solution is correct!
Solution 5:
370, 992, 663
Verification:
(370 + 992 + 663) / 3 = 2025 / 3 ≈ 675
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 2025 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.