What three numbers have an average of 345?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 345. This means if we add these three numbers together and divide by 3, we should get 345.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 345 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 345 * 3 = x + y + z
- So, the sum of our three numbers should be: 1035
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1035.
Solution 1:
345, 345, 345
Verification:
(345 + 345 + 345) / 3 = 1035 / 3 ≈ 345
This solution is correct!
Solution 2:
345, 345, 345
Verification:
(345 + 345 + 345) / 3 = 1035 / 3 ≈ 345
This solution is correct!
Solution 3:
717, 203, 115
Verification:
(717 + 203 + 115) / 3 = 1035 / 3 ≈ 345
This solution is correct!
Solution 4:
361, 516, 158
Verification:
(361 + 516 + 158) / 3 = 1035 / 3 ≈ 345
This solution is correct!
Solution 5:
290, 695, 50
Verification:
(290 + 695 + 50) / 3 = 1035 / 3 ≈ 345
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 1035 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.