What three numbers have an average of 233?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 233. This means if we add these three numbers together and divide by 3, we should get 233.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 233 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 233 * 3 = x + y + z
- So, the sum of our three numbers should be: 699
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 699.
Solution 1:
233, 233, 233
Verification:
(233 + 233 + 233) / 3 = 699 / 3 ≈ 233
This solution is correct!
Solution 2:
233, 233, 233
Verification:
(233 + 233 + 233) / 3 = 699 / 3 ≈ 233
This solution is correct!
Solution 3:
465, 77, 157
Verification:
(465 + 77 + 157) / 3 = 699 / 3 ≈ 233
This solution is correct!
Solution 4:
649, 42, 8
Verification:
(649 + 42 + 8) / 3 = 699 / 3 ≈ 233
This solution is correct!
Solution 5:
1, 252, 446
Verification:
(1 + 252 + 446) / 3 = 699 / 3 ≈ 233
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 699 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.