What three numbers have an average of 320?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 320. This means if we add these three numbers together and divide by 3, we should get 320.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 320 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 320 * 3 = x + y + z
- So, the sum of our three numbers should be: 960
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 960.
Solution 1:
320, 320, 320
Verification:
(320 + 320 + 320) / 3 = 960 / 3 ≈ 320
This solution is correct!
Solution 2:
320, 320, 320
Verification:
(320 + 320 + 320) / 3 = 960 / 3 ≈ 320
This solution is correct!
Solution 3:
566, 297, 97
Verification:
(566 + 297 + 97) / 3 = 960 / 3 ≈ 320
This solution is correct!
Solution 4:
578, 341, 41
Verification:
(578 + 341 + 41) / 3 = 960 / 3 ≈ 320
This solution is correct!
Solution 5:
96, 843, 21
Verification:
(96 + 843 + 21) / 3 = 960 / 3 ≈ 320
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 960 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.