What three numbers have an average of 111?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 111. This means if we add these three numbers together and divide by 3, we should get 111.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 111 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 111 * 3 = x + y + z
- So, the sum of our three numbers should be: 333
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 333.
Solution 1:
111, 111, 111
Verification:
(111 + 111 + 111) / 3 = 333 / 3 ≈ 111
This solution is correct!
Solution 2:
111, 111, 111
Verification:
(111 + 111 + 111) / 3 = 333 / 3 ≈ 111
This solution is correct!
Solution 3:
71, 128, 134
Verification:
(71 + 128 + 134) / 3 = 333 / 3 ≈ 111
This solution is correct!
Solution 4:
73, 138, 122
Verification:
(73 + 138 + 122) / 3 = 333 / 3 ≈ 111
This solution is correct!
Solution 5:
51, 111, 171
Verification:
(51 + 111 + 171) / 3 = 333 / 3 ≈ 111
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 333 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.