What three numbers have an average of 40?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 40. This means if we add these three numbers together and divide by 3, we should get 40.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 40 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 40 * 3 = x + y + z
- So, the sum of our three numbers should be: 120
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 120.
Solution 1:
40, 40, 40
Verification:
(40 + 40 + 40) / 3 = 120 / 3 ≈ 40
This solution is correct!
Solution 2:
40, 40, 40
Verification:
(40 + 40 + 40) / 3 = 120 / 3 ≈ 40
This solution is correct!
Solution 3:
54, 27, 39
Verification:
(54 + 27 + 39) / 3 = 120 / 3 ≈ 40
This solution is correct!
Solution 4:
78, 1, 41
Verification:
(78 + 1 + 41) / 3 = 120 / 3 ≈ 40
This solution is correct!
Solution 5:
16, 43, 61
Verification:
(16 + 43 + 61) / 3 = 120 / 3 ≈ 40
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 120 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.