What three numbers have an average of 103?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 103. This means if we add these three numbers together and divide by 3, we should get 103.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 103 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 103 * 3 = x + y + z
- So, the sum of our three numbers should be: 309
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 309.
Solution 1:
103, 103, 103
Verification:
(103 + 103 + 103) / 3 = 309 / 3 ≈ 103
This solution is correct!
Solution 2:
103, 103, 103
Verification:
(103 + 103 + 103) / 3 = 309 / 3 ≈ 103
This solution is correct!
Solution 3:
292, 5, 12
Verification:
(292 + 5 + 12) / 3 = 309 / 3 ≈ 103
This solution is correct!
Solution 4:
55, 201, 53
Verification:
(55 + 201 + 53) / 3 = 309 / 3 ≈ 103
This solution is correct!
Solution 5:
159, 105, 45
Verification:
(159 + 105 + 45) / 3 = 309 / 3 ≈ 103
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 309 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.