What three numbers have an average of 960?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 960. This means if we add these three numbers together and divide by 3, we should get 960.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 960 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 960 * 3 = x + y + z
- So, the sum of our three numbers should be: 2880
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2880.
Solution 1:
960, 960, 960
Verification:
(960 + 960 + 960) / 3 = 2880 / 3 ≈ 960
This solution is correct!
Solution 2:
960, 960, 960
Verification:
(960 + 960 + 960) / 3 = 2880 / 3 ≈ 960
This solution is correct!
Solution 3:
1455, 729, 696
Verification:
(1455 + 729 + 696) / 3 = 2880 / 3 ≈ 960
This solution is correct!
Solution 4:
2601, 251, 28
Verification:
(2601 + 251 + 28) / 3 = 2880 / 3 ≈ 960
This solution is correct!
Solution 5:
1235, 446, 1199
Verification:
(1235 + 446 + 1199) / 3 = 2880 / 3 ≈ 960
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 2880 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.