What three numbers have an average of 828?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 828. This means if we add these three numbers together and divide by 3, we should get 828.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 828 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 828 * 3 = x + y + z
- So, the sum of our three numbers should be: 2484
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2484.
Solution 1:
828, 828, 828
Verification:
(828 + 828 + 828) / 3 = 2484 / 3 ≈ 828
This solution is correct!
Solution 2:
828, 828, 828
Verification:
(828 + 828 + 828) / 3 = 2484 / 3 ≈ 828
This solution is correct!
Solution 3:
1397, 189, 898
Verification:
(1397 + 189 + 898) / 3 = 2484 / 3 ≈ 828
This solution is correct!
Solution 4:
1589, 173, 722
Verification:
(1589 + 173 + 722) / 3 = 2484 / 3 ≈ 828
This solution is correct!
Solution 5:
1508, 887, 89
Verification:
(1508 + 887 + 89) / 3 = 2484 / 3 ≈ 828
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 2484 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.