What three numbers have an average of 191?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 191. This means if we add these three numbers together and divide by 3, we should get 191.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 191 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 191 * 3 = x + y + z
- So, the sum of our three numbers should be: 573
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 573.
Solution 1:
191, 191, 191
Verification:
(191 + 191 + 191) / 3 = 573 / 3 ≈ 191
This solution is correct!
Solution 2:
191, 191, 191
Verification:
(191 + 191 + 191) / 3 = 573 / 3 ≈ 191
This solution is correct!
Solution 3:
43, 242, 288
Verification:
(43 + 242 + 288) / 3 = 573 / 3 ≈ 191
This solution is correct!
Solution 4:
421, 8, 144
Verification:
(421 + 8 + 144) / 3 = 573 / 3 ≈ 191
This solution is correct!
Solution 5:
183, 225, 165
Verification:
(183 + 225 + 165) / 3 = 573 / 3 ≈ 191
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 573 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.