What three numbers have an average of 43?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 43. This means if we add these three numbers together and divide by 3, we should get 43.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 43 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 43 * 3 = x + y + z
- So, the sum of our three numbers should be: 129
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 129.
Solution 1:
43, 43, 43
Verification:
(43 + 43 + 43) / 3 = 129 / 3 ≈ 43
This solution is correct!
Solution 2:
43, 43, 43
Verification:
(43 + 43 + 43) / 3 = 129 / 3 ≈ 43
This solution is correct!
Solution 3:
101, 13, 15
Verification:
(101 + 13 + 15) / 3 = 129 / 3 ≈ 43
This solution is correct!
Solution 4:
21, 14, 94
Verification:
(21 + 14 + 94) / 3 = 129 / 3 ≈ 43
This solution is correct!
Solution 5:
31, 49, 49
Verification:
(31 + 49 + 49) / 3 = 129 / 3 ≈ 43
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 129 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.