What three numbers have an average of 803?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 803. This means if we add these three numbers together and divide by 3, we should get 803.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 803 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 803 * 3 = x + y + z
- So, the sum of our three numbers should be: 2409
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2409.
Solution 1:
803, 803, 803
Verification:
(803 + 803 + 803) / 3 = 2409 / 3 ≈ 803
This solution is correct!
Solution 2:
803, 803, 803
Verification:
(803 + 803 + 803) / 3 = 2409 / 3 ≈ 803
This solution is correct!
Solution 3:
2096, 294, 19
Verification:
(2096 + 294 + 19) / 3 = 2409 / 3 ≈ 803
This solution is correct!
Solution 4:
378, 765, 1266
Verification:
(378 + 765 + 1266) / 3 = 2409 / 3 ≈ 803
This solution is correct!
Solution 5:
1762, 528, 119
Verification:
(1762 + 528 + 119) / 3 = 2409 / 3 ≈ 803
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 2409 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.