What three numbers have an average of 46?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 46. This means if we add these three numbers together and divide by 3, we should get 46.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 46 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 46 * 3 = x + y + z
- So, the sum of our three numbers should be: 138
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 138.
Solution 1:
46, 46, 46
Verification:
(46 + 46 + 46) / 3 = 138 / 3 ≈ 46
This solution is correct!
Solution 2:
46, 46, 46
Verification:
(46 + 46 + 46) / 3 = 138 / 3 ≈ 46
This solution is correct!
Solution 3:
37, 6, 95
Verification:
(37 + 6 + 95) / 3 = 138 / 3 ≈ 46
This solution is correct!
Solution 4:
49, 28, 61
Verification:
(49 + 28 + 61) / 3 = 138 / 3 ≈ 46
This solution is correct!
Solution 5:
69, 41, 28
Verification:
(69 + 41 + 28) / 3 = 138 / 3 ≈ 46
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 138 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.