What three numbers have an average of 226?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 226. This means if we add these three numbers together and divide by 3, we should get 226.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 226 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 226 * 3 = x + y + z
- So, the sum of our three numbers should be: 678
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 678.
Solution 1:
226, 226, 226
Verification:
(226 + 226 + 226) / 3 = 678 / 3 ≈ 226
This solution is correct!
Solution 2:
226, 226, 226
Verification:
(226 + 226 + 226) / 3 = 678 / 3 ≈ 226
This solution is correct!
Solution 3:
45, 84, 549
Verification:
(45 + 84 + 549) / 3 = 678 / 3 ≈ 226
This solution is correct!
Solution 4:
211, 100, 367
Verification:
(211 + 100 + 367) / 3 = 678 / 3 ≈ 226
This solution is correct!
Solution 5:
195, 79, 404
Verification:
(195 + 79 + 404) / 3 = 678 / 3 ≈ 226
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 678 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.