What three numbers have an average of 390?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 390. This means if we add these three numbers together and divide by 3, we should get 390.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 390 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 390 * 3 = x + y + z
- So, the sum of our three numbers should be: 1170
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1170.
Solution 1:
390, 390, 390
Verification:
(390 + 390 + 390) / 3 = 1170 / 3 ≈ 390
This solution is correct!
Solution 2:
390, 390, 390
Verification:
(390 + 390 + 390) / 3 = 1170 / 3 ≈ 390
This solution is correct!
Solution 3:
862, 99, 209
Verification:
(862 + 99 + 209) / 3 = 1170 / 3 ≈ 390
This solution is correct!
Solution 4:
356, 172, 642
Verification:
(356 + 172 + 642) / 3 = 1170 / 3 ≈ 390
This solution is correct!
Solution 5:
402, 764, 4
Verification:
(402 + 764 + 4) / 3 = 1170 / 3 ≈ 390
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 1170 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.