What three numbers have an average of 101?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 101. This means if we add these three numbers together and divide by 3, we should get 101.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 101 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 101 * 3 = x + y + z
- So, the sum of our three numbers should be: 303
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 303.
Solution 1:
101, 101, 101
Verification:
(101 + 101 + 101) / 3 = 303 / 3 ≈ 101
This solution is correct!
Solution 2:
101, 101, 101
Verification:
(101 + 101 + 101) / 3 = 303 / 3 ≈ 101
This solution is correct!
Solution 3:
29, 90, 184
Verification:
(29 + 90 + 184) / 3 = 303 / 3 ≈ 101
This solution is correct!
Solution 4:
175, 28, 100
Verification:
(175 + 28 + 100) / 3 = 303 / 3 ≈ 101
This solution is correct!
Solution 5:
101, 3, 199
Verification:
(101 + 3 + 199) / 3 = 303 / 3 ≈ 101
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 303 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.