What three numbers have an average of 114?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 114. This means if we add these three numbers together and divide by 3, we should get 114.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 114 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 114 * 3 = x + y + z
- So, the sum of our three numbers should be: 342
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 342.
Solution 1:
114, 114, 114
Verification:
(114 + 114 + 114) / 3 = 342 / 3 ≈ 114
This solution is correct!
Solution 2:
114, 114, 114
Verification:
(114 + 114 + 114) / 3 = 342 / 3 ≈ 114
This solution is correct!
Solution 3:
100, 240, 2
Verification:
(100 + 240 + 2) / 3 = 342 / 3 ≈ 114
This solution is correct!
Solution 4:
58, 143, 141
Verification:
(58 + 143 + 141) / 3 = 342 / 3 ≈ 114
This solution is correct!
Solution 5:
39, 264, 39
Verification:
(39 + 264 + 39) / 3 = 342 / 3 ≈ 114
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 342 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.