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:
1463, 658, 291
Verification:
(1463 + 658 + 291) / 3 = 2412 / 3 ≈ 804
This solution is correct!
Solution 4:
1658, 210, 544
Verification:
(1658 + 210 + 544) / 3 = 2412 / 3 ≈ 804
This solution is correct!
Solution 5:
1615, 564, 233
Verification:
(1615 + 564 + 233) / 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.