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:
948, 8, 4
Verification:
(948 + 8 + 4) / 3 = 960 / 3 ≈ 320
This solution is correct!
Solution 4:
128, 714, 118
Verification:
(128 + 714 + 118) / 3 = 960 / 3 ≈ 320
This solution is correct!
Solution 5:
617, 306, 37
Verification:
(617 + 306 + 37) / 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.