What three numbers have an average of 224?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 224. This means if we add these three numbers together and divide by 3, we should get 224.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 224 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 224 * 3 = x + y + z
- So, the sum of our three numbers should be: 672
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 672.
Solution 1:
224, 224, 224
Verification:
(224 + 224 + 224) / 3 = 672 / 3 ≈ 224
This solution is correct!
Solution 2:
224, 224, 224
Verification:
(224 + 224 + 224) / 3 = 672 / 3 ≈ 224
This solution is correct!
Solution 3:
114, 22, 536
Verification:
(114 + 22 + 536) / 3 = 672 / 3 ≈ 224
This solution is correct!
Solution 4:
591, 3, 78
Verification:
(591 + 3 + 78) / 3 = 672 / 3 ≈ 224
This solution is correct!
Solution 5:
414, 154, 104
Verification:
(414 + 154 + 104) / 3 = 672 / 3 ≈ 224
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 672 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.