What three numbers have an average of 65?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 65. This means if we add these three numbers together and divide by 3, we should get 65.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 65 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 65 * 3 = x + y + z
- So, the sum of our three numbers should be: 195
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 195.
Solution 1:
65, 65, 65
Verification:
(65 + 65 + 65) / 3 = 195 / 3 ≈ 65
This solution is correct!
Solution 2:
65, 65, 65
Verification:
(65 + 65 + 65) / 3 = 195 / 3 ≈ 65
This solution is correct!
Solution 3:
10, 45, 140
Verification:
(10 + 45 + 140) / 3 = 195 / 3 ≈ 65
This solution is correct!
Solution 4:
72, 50, 73
Verification:
(72 + 50 + 73) / 3 = 195 / 3 ≈ 65
This solution is correct!
Solution 5:
80, 25, 90
Verification:
(80 + 25 + 90) / 3 = 195 / 3 ≈ 65
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 195 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.