What three numbers have an average of 112?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 112. This means if we add these three numbers together and divide by 3, we should get 112.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 112 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 112 * 3 = x + y + z
- So, the sum of our three numbers should be: 336
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 336.
Solution 1:
112, 112, 112
Verification:
(112 + 112 + 112) / 3 = 336 / 3 ≈ 112
This solution is correct!
Solution 2:
112, 112, 112
Verification:
(112 + 112 + 112) / 3 = 336 / 3 ≈ 112
This solution is correct!
Solution 3:
120, 82, 134
Verification:
(120 + 82 + 134) / 3 = 336 / 3 ≈ 112
This solution is correct!
Solution 4:
67, 15, 254
Verification:
(67 + 15 + 254) / 3 = 336 / 3 ≈ 112
This solution is correct!
Solution 5:
244, 84, 8
Verification:
(244 + 84 + 8) / 3 = 336 / 3 ≈ 112
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 336 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.