What three numbers have an average of 107?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 107. This means if we add these three numbers together and divide by 3, we should get 107.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 107 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 107 * 3 = x + y + z
- So, the sum of our three numbers should be: 321
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 321.
Solution 1:
107, 107, 107
Verification:
(107 + 107 + 107) / 3 = 321 / 3 ≈ 107
This solution is correct!
Solution 2:
107, 107, 107
Verification:
(107 + 107 + 107) / 3 = 321 / 3 ≈ 107
This solution is correct!
Solution 3:
67, 221, 33
Verification:
(67 + 221 + 33) / 3 = 321 / 3 ≈ 107
This solution is correct!
Solution 4:
210, 73, 38
Verification:
(210 + 73 + 38) / 3 = 321 / 3 ≈ 107
This solution is correct!
Solution 5:
1, 286, 34
Verification:
(1 + 286 + 34) / 3 = 321 / 3 ≈ 107
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 321 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.