What three numbers have an average of 104?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 104. This means if we add these three numbers together and divide by 3, we should get 104.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 104 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 104 * 3 = x + y + z
- So, the sum of our three numbers should be: 312
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 312.
Solution 1:
104, 104, 104
Verification:
(104 + 104 + 104) / 3 = 312 / 3 ≈ 104
This solution is correct!
Solution 2:
104, 104, 104
Verification:
(104 + 104 + 104) / 3 = 312 / 3 ≈ 104
This solution is correct!
Solution 3:
32, 157, 123
Verification:
(32 + 157 + 123) / 3 = 312 / 3 ≈ 104
This solution is correct!
Solution 4:
69, 5, 238
Verification:
(69 + 5 + 238) / 3 = 312 / 3 ≈ 104
This solution is correct!
Solution 5:
274, 19, 19
Verification:
(274 + 19 + 19) / 3 = 312 / 3 ≈ 104
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 312 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.