What three numbers have an average of 848?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 848. This means if we add these three numbers together and divide by 3, we should get 848.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 848 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 848 * 3 = x + y + z
- So, the sum of our three numbers should be: 2544
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2544.
Solution 1:
848, 848, 848
Verification:
(848 + 848 + 848) / 3 = 2544 / 3 ≈ 848
This solution is correct!
Solution 2:
848, 848, 848
Verification:
(848 + 848 + 848) / 3 = 2544 / 3 ≈ 848
This solution is correct!
Solution 3:
455, 1286, 803
Verification:
(455 + 1286 + 803) / 3 = 2544 / 3 ≈ 848
This solution is correct!
Solution 4:
1304, 557, 683
Verification:
(1304 + 557 + 683) / 3 = 2544 / 3 ≈ 848
This solution is correct!
Solution 5:
2414, 83, 47
Verification:
(2414 + 83 + 47) / 3 = 2544 / 3 ≈ 848
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 2544 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.