What three numbers have an average of 45?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 45. This means if we add these three numbers together and divide by 3, we should get 45.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 45 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 45 * 3 = x + y + z
- So, the sum of our three numbers should be: 135
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 135.
Solution 1:
45, 45, 45
Verification:
(45 + 45 + 45) / 3 = 135 / 3 ≈ 45
This solution is correct!
Solution 2:
45, 45, 45
Verification:
(45 + 45 + 45) / 3 = 135 / 3 ≈ 45
This solution is correct!
Solution 3:
78, 47, 10
Verification:
(78 + 47 + 10) / 3 = 135 / 3 ≈ 45
This solution is correct!
Solution 4:
78, 48, 9
Verification:
(78 + 48 + 9) / 3 = 135 / 3 ≈ 45
This solution is correct!
Solution 5:
93, 7, 35
Verification:
(93 + 7 + 35) / 3 = 135 / 3 ≈ 45
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 135 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.