What three numbers have an average of 223?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 223. This means if we add these three numbers together and divide by 3, we should get 223.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 223 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 223 * 3 = x + y + z
- So, the sum of our three numbers should be: 669
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 669.
Solution 1:
223, 223, 223
Verification:
(223 + 223 + 223) / 3 = 669 / 3 ≈ 223
This solution is correct!
Solution 2:
223, 223, 223
Verification:
(223 + 223 + 223) / 3 = 669 / 3 ≈ 223
This solution is correct!
Solution 3:
78, 334, 257
Verification:
(78 + 334 + 257) / 3 = 669 / 3 ≈ 223
This solution is correct!
Solution 4:
183, 432, 54
Verification:
(183 + 432 + 54) / 3 = 669 / 3 ≈ 223
This solution is correct!
Solution 5:
408, 150, 111
Verification:
(408 + 150 + 111) / 3 = 669 / 3 ≈ 223
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 669 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.