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:
85, 29, 12
Verification:
(85 + 29 + 12) / 3 = 126 / 3 ≈ 42
This solution is correct!
Solution 4:
1, 58, 67
Verification:
(1 + 58 + 67) / 3 = 126 / 3 ≈ 42
This solution is correct!
Solution 5:
46, 66, 14
Verification:
(46 + 66 + 14) / 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.