What three numbers have an average of 42?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 42. This means if we add these three numbers together and divide by 3, we should get 42.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 42 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 42 * 3 = x + y + z
- So, the sum of our three numbers should be: 126
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 126.
Solution 1:
42, 42, 42
Verification:
(42 + 42 + 42) / 3 = 126 / 3 ≈ 42
This solution is correct!
Solution 2:
42, 42, 42
Verification:
(42 + 42 + 42) / 3 = 126 / 3 ≈ 42
This solution is correct!
Solution 3:
64, 13, 49
Verification:
(64 + 13 + 49) / 3 = 126 / 3 ≈ 42
This solution is correct!
Solution 4:
45, 41, 40
Verification:
(45 + 41 + 40) / 3 = 126 / 3 ≈ 42
This solution is correct!
Solution 5:
37, 58, 31
Verification:
(37 + 58 + 31) / 3 = 126 / 3 ≈ 42
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 126 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.