What three numbers have an average of 845?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 845. This means if we add these three numbers together and divide by 3, we should get 845.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 845 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 845 * 3 = x + y + z
- So, the sum of our three numbers should be: 2535
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2535.
Solution 1:
845, 845, 845
Verification:
(845 + 845 + 845) / 3 = 2535 / 3 ≈ 845
This solution is correct!
Solution 2:
845, 845, 845
Verification:
(845 + 845 + 845) / 3 = 2535 / 3 ≈ 845
This solution is correct!
Solution 3:
122, 1419, 994
Verification:
(122 + 1419 + 994) / 3 = 2535 / 3 ≈ 845
This solution is correct!
Solution 4:
1260, 48, 1227
Verification:
(1260 + 48 + 1227) / 3 = 2535 / 3 ≈ 845
This solution is correct!
Solution 5:
586, 1844, 105
Verification:
(586 + 1844 + 105) / 3 = 2535 / 3 ≈ 845
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 2535 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.