What three numbers have an average of 110?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 110. This means if we add these three numbers together and divide by 3, we should get 110.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 110 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 110 * 3 = x + y + z
- So, the sum of our three numbers should be: 330
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 330.
Solution 1:
110, 110, 110
Verification:
(110 + 110 + 110) / 3 = 330 / 3 ≈ 110
This solution is correct!
Solution 2:
110, 110, 110
Verification:
(110 + 110 + 110) / 3 = 330 / 3 ≈ 110
This solution is correct!
Solution 3:
274, 23, 33
Verification:
(274 + 23 + 33) / 3 = 330 / 3 ≈ 110
This solution is correct!
Solution 4:
46, 97, 187
Verification:
(46 + 97 + 187) / 3 = 330 / 3 ≈ 110
This solution is correct!
Solution 5:
166, 16, 148
Verification:
(166 + 16 + 148) / 3 = 330 / 3 ≈ 110
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 330 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.