What three numbers have an average of 162?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 162. This means if we add these three numbers together and divide by 3, we should get 162.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 162 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 162 * 3 = x + y + z
- So, the sum of our three numbers should be: 486
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 486.
Solution 1:
162, 162, 162
Verification:
(162 + 162 + 162) / 3 = 486 / 3 ≈ 162
This solution is correct!
Solution 2:
162, 162, 162
Verification:
(162 + 162 + 162) / 3 = 486 / 3 ≈ 162
This solution is correct!
Solution 3:
207, 3, 276
Verification:
(207 + 3 + 276) / 3 = 486 / 3 ≈ 162
This solution is correct!
Solution 4:
199, 147, 140
Verification:
(199 + 147 + 140) / 3 = 486 / 3 ≈ 162
This solution is correct!
Solution 5:
126, 27, 333
Verification:
(126 + 27 + 333) / 3 = 486 / 3 ≈ 162
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 486 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.