What three numbers have an average of 825?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 825. This means if we add these three numbers together and divide by 3, we should get 825.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 825 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 825 * 3 = x + y + z
- So, the sum of our three numbers should be: 2475
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2475.
Solution 1:
825, 825, 825
Verification:
(825 + 825 + 825) / 3 = 2475 / 3 ≈ 825
This solution is correct!
Solution 2:
825, 825, 825
Verification:
(825 + 825 + 825) / 3 = 2475 / 3 ≈ 825
This solution is correct!
Solution 3:
2057, 162, 256
Verification:
(2057 + 162 + 256) / 3 = 2475 / 3 ≈ 825
This solution is correct!
Solution 4:
305, 1068, 1102
Verification:
(305 + 1068 + 1102) / 3 = 2475 / 3 ≈ 825
This solution is correct!
Solution 5:
1081, 887, 507
Verification:
(1081 + 887 + 507) / 3 = 2475 / 3 ≈ 825
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 2475 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.