What three numbers have an average of 146?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 146. This means if we add these three numbers together and divide by 3, we should get 146.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 146 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 146 * 3 = x + y + z
- So, the sum of our three numbers should be: 438
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 438.
Solution 1:
146, 146, 146
Verification:
(146 + 146 + 146) / 3 = 438 / 3 ≈ 146
This solution is correct!
Solution 2:
146, 146, 146
Verification:
(146 + 146 + 146) / 3 = 438 / 3 ≈ 146
This solution is correct!
Solution 3:
104, 38, 296
Verification:
(104 + 38 + 296) / 3 = 438 / 3 ≈ 146
This solution is correct!
Solution 4:
111, 131, 196
Verification:
(111 + 131 + 196) / 3 = 438 / 3 ≈ 146
This solution is correct!
Solution 5:
238, 26, 174
Verification:
(238 + 26 + 174) / 3 = 438 / 3 ≈ 146
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 438 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.