What three numbers have an average of 32?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 32. This means if we add these three numbers together and divide by 3, we should get 32.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 32 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 32 * 3 = x + y + z
- So, the sum of our three numbers should be: 96
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 96.
Solution 1:
32, 32, 32
Verification:
(32 + 32 + 32) / 3 = 96 / 3 ≈ 32
This solution is correct!
Solution 2:
32, 32, 32
Verification:
(32 + 32 + 32) / 3 = 96 / 3 ≈ 32
This solution is correct!
Solution 3:
58, 19, 19
Verification:
(58 + 19 + 19) / 3 = 96 / 3 ≈ 32
This solution is correct!
Solution 4:
6, 55, 35
Verification:
(6 + 55 + 35) / 3 = 96 / 3 ≈ 32
This solution is correct!
Solution 5:
84, 11, 1
Verification:
(84 + 11 + 1) / 3 = 96 / 3 ≈ 32
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 96 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.