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:
38, 350, 185
Verification:
(38 + 350 + 185) / 3 = 573 / 3 ≈ 191
This solution is correct!
Solution 4:
11, 339, 223
Verification:
(11 + 339 + 223) / 3 = 573 / 3 ≈ 191
This solution is correct!
Solution 5:
276, 182, 115
Verification:
(276 + 182 + 115) / 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.