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:
56, 30, 10
Verification:
(56 + 30 + 10) / 3 = 96 / 3 ≈ 32
This solution is correct!
Solution 4:
10, 69, 17
Verification:
(10 + 69 + 17) / 3 = 96 / 3 ≈ 32
This solution is correct!
Solution 5:
26, 22, 48
Verification:
(26 + 22 + 48) / 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.