What three numbers have an average of 47?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 47. This means if we add these three numbers together and divide by 3, we should get 47.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 47 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 47 * 3 = x + y + z
- So, the sum of our three numbers should be: 141
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 141.
Solution 1:
47, 47, 47
Verification:
(47 + 47 + 47) / 3 = 141 / 3 ≈ 47
This solution is correct!
Solution 2:
47, 47, 47
Verification:
(47 + 47 + 47) / 3 = 141 / 3 ≈ 47
This solution is correct!
Solution 3:
13, 22, 106
Verification:
(13 + 22 + 106) / 3 = 141 / 3 ≈ 47
This solution is correct!
Solution 4:
119, 7, 15
Verification:
(119 + 7 + 15) / 3 = 141 / 3 ≈ 47
This solution is correct!
Solution 5:
87, 6, 48
Verification:
(87 + 6 + 48) / 3 = 141 / 3 ≈ 47
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 141 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.