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:
28, 222, 62
Verification:
(28 + 222 + 62) / 3 = 312 / 3 ≈ 104
This solution is correct!
Solution 4:
282, 22, 8
Verification:
(282 + 22 + 8) / 3 = 312 / 3 ≈ 104
This solution is correct!
Solution 5:
22, 10, 280
Verification:
(22 + 10 + 280) / 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.