What three numbers have an average of 145?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 145. This means if we add these three numbers together and divide by 3, we should get 145.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 145 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 145 * 3 = x + y + z
- So, the sum of our three numbers should be: 435
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 435.
Solution 1:
145, 145, 145
Verification:
(145 + 145 + 145) / 3 = 435 / 3 ≈ 145
This solution is correct!
Solution 2:
145, 145, 145
Verification:
(145 + 145 + 145) / 3 = 435 / 3 ≈ 145
This solution is correct!
Solution 3:
355, 4, 76
Verification:
(355 + 4 + 76) / 3 = 435 / 3 ≈ 145
This solution is correct!
Solution 4:
388, 5, 42
Verification:
(388 + 5 + 42) / 3 = 435 / 3 ≈ 145
This solution is correct!
Solution 5:
74, 64, 297
Verification:
(74 + 64 + 297) / 3 = 435 / 3 ≈ 145
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 435 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.