What three numbers have an average of 100?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 100. This means if we add these three numbers together and divide by 3, we should get 100.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 100 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 100 * 3 = x + y + z
- So, the sum of our three numbers should be: 300
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 300.
Solution 1:
100, 100, 100
Verification:
(100 + 100 + 100) / 3 = 300 / 3 ≈ 100
This solution is correct!
Solution 2:
100, 100, 100
Verification:
(100 + 100 + 100) / 3 = 300 / 3 ≈ 100
This solution is correct!
Solution 3:
272, 27, 1
Verification:
(272 + 27 + 1) / 3 = 300 / 3 ≈ 100
This solution is correct!
Solution 4:
42, 11, 247
Verification:
(42 + 11 + 247) / 3 = 300 / 3 ≈ 100
This solution is correct!
Solution 5:
182, 29, 89
Verification:
(182 + 29 + 89) / 3 = 300 / 3 ≈ 100
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 300 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.