What three numbers have an average of 804?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 804. This means if we add these three numbers together and divide by 3, we should get 804.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 804 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 804 * 3 = x + y + z
- So, the sum of our three numbers should be: 2412
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2412.
Solution 1:
804, 804, 804
Verification:
(804 + 804 + 804) / 3 = 2412 / 3 ≈ 804
This solution is correct!
Solution 2:
804, 804, 804
Verification:
(804 + 804 + 804) / 3 = 2412 / 3 ≈ 804
This solution is correct!
Solution 3:
791, 512, 1109
Verification:
(791 + 512 + 1109) / 3 = 2412 / 3 ≈ 804
This solution is correct!
Solution 4:
1719, 179, 514
Verification:
(1719 + 179 + 514) / 3 = 2412 / 3 ≈ 804
This solution is correct!
Solution 5:
2278, 63, 71
Verification:
(2278 + 63 + 71) / 3 = 2412 / 3 ≈ 804
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 2412 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.