What three numbers have an average of 480?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 480. This means if we add these three numbers together and divide by 3, we should get 480.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 480 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 480 * 3 = x + y + z
- So, the sum of our three numbers should be: 1440
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1440.
Solution 1:
480, 480, 480
Verification:
(480 + 480 + 480) / 3 = 1440 / 3 ≈ 480
This solution is correct!
Solution 2:
480, 480, 480
Verification:
(480 + 480 + 480) / 3 = 1440 / 3 ≈ 480
This solution is correct!
Solution 3:
106, 69, 1265
Verification:
(106 + 69 + 1265) / 3 = 1440 / 3 ≈ 480
This solution is correct!
Solution 4:
1410, 10, 20
Verification:
(1410 + 10 + 20) / 3 = 1440 / 3 ≈ 480
This solution is correct!
Solution 5:
713, 169, 558
Verification:
(713 + 169 + 558) / 3 = 1440 / 3 ≈ 480
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 1440 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.