What three numbers have an average of 197?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 197. This means if we add these three numbers together and divide by 3, we should get 197.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 197 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 197 * 3 = x + y + z
- So, the sum of our three numbers should be: 591
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 591.
Solution 1:
197, 197, 197
Verification:
(197 + 197 + 197) / 3 = 591 / 3 ≈ 197
This solution is correct!
Solution 2:
197, 197, 197
Verification:
(197 + 197 + 197) / 3 = 591 / 3 ≈ 197
This solution is correct!
Solution 3:
538, 18, 35
Verification:
(538 + 18 + 35) / 3 = 591 / 3 ≈ 197
This solution is correct!
Solution 4:
357, 212, 22
Verification:
(357 + 212 + 22) / 3 = 591 / 3 ≈ 197
This solution is correct!
Solution 5:
331, 253, 7
Verification:
(331 + 253 + 7) / 3 = 591 / 3 ≈ 197
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 591 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.