What three numbers have an average of 393?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 393. This means if we add these three numbers together and divide by 3, we should get 393.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 393 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 393 * 3 = x + y + z
- So, the sum of our three numbers should be: 1179
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1179.
Solution 1:
393, 393, 393
Verification:
(393 + 393 + 393) / 3 = 1179 / 3 ≈ 393
This solution is correct!
Solution 2:
393, 393, 393
Verification:
(393 + 393 + 393) / 3 = 1179 / 3 ≈ 393
This solution is correct!
Solution 3:
659, 445, 75
Verification:
(659 + 445 + 75) / 3 = 1179 / 3 ≈ 393
This solution is correct!
Solution 4:
359, 763, 57
Verification:
(359 + 763 + 57) / 3 = 1179 / 3 ≈ 393
This solution is correct!
Solution 5:
875, 191, 113
Verification:
(875 + 191 + 113) / 3 = 1179 / 3 ≈ 393
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 1179 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.