What three numbers have an average of 33?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 33. This means if we add these three numbers together and divide by 3, we should get 33.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 33 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 33 * 3 = x + y + z
- So, the sum of our three numbers should be: 99
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 99.
Solution 1:
33, 33, 33
Verification:
(33 + 33 + 33) / 3 = 99 / 3 ≈ 33
This solution is correct!
Solution 2:
33, 33, 33
Verification:
(33 + 33 + 33) / 3 = 99 / 3 ≈ 33
This solution is correct!
Solution 3:
43, 29, 27
Verification:
(43 + 29 + 27) / 3 = 99 / 3 ≈ 33
This solution is correct!
Solution 4:
61, 16, 22
Verification:
(61 + 16 + 22) / 3 = 99 / 3 ≈ 33
This solution is correct!
Solution 5:
13, 15, 71
Verification:
(13 + 15 + 71) / 3 = 99 / 3 ≈ 33
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 99 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.