What three numbers have an average of 64?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 64. This means if we add these three numbers together and divide by 3, we should get 64.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 64 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 64 * 3 = x + y + z
- So, the sum of our three numbers should be: 192
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 192.
Solution 1:
64, 64, 64
Verification:
(64 + 64 + 64) / 3 = 192 / 3 ≈ 64
This solution is correct!
Solution 2:
64, 64, 64
Verification:
(64 + 64 + 64) / 3 = 192 / 3 ≈ 64
This solution is correct!
Solution 3:
148, 36, 8
Verification:
(148 + 36 + 8) / 3 = 192 / 3 ≈ 64
This solution is correct!
Solution 4:
139, 14, 39
Verification:
(139 + 14 + 39) / 3 = 192 / 3 ≈ 64
This solution is correct!
Solution 5:
38, 36, 118
Verification:
(38 + 36 + 118) / 3 = 192 / 3 ≈ 64
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 192 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.