What three numbers have an average of 193?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 193. This means if we add these three numbers together and divide by 3, we should get 193.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 193 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 193 * 3 = x + y + z
- So, the sum of our three numbers should be: 579
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 579.
Solution 1:
193, 193, 193
Verification:
(193 + 193 + 193) / 3 = 579 / 3 ≈ 193
This solution is correct!
Solution 2:
193, 193, 193
Verification:
(193 + 193 + 193) / 3 = 579 / 3 ≈ 193
This solution is correct!
Solution 3:
21, 123, 435
Verification:
(21 + 123 + 435) / 3 = 579 / 3 ≈ 193
This solution is correct!
Solution 4:
31, 146, 402
Verification:
(31 + 146 + 402) / 3 = 579 / 3 ≈ 193
This solution is correct!
Solution 5:
282, 210, 87
Verification:
(282 + 210 + 87) / 3 = 579 / 3 ≈ 193
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 579 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.