What three numbers have an average of 164?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 164. This means if we add these three numbers together and divide by 3, we should get 164.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 164 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 164 * 3 = x + y + z
- So, the sum of our three numbers should be: 492
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 492.
Solution 1:
164, 164, 164
Verification:
(164 + 164 + 164) / 3 = 492 / 3 ≈ 164
This solution is correct!
Solution 2:
164, 164, 164
Verification:
(164 + 164 + 164) / 3 = 492 / 3 ≈ 164
This solution is correct!
Solution 3:
29, 344, 119
Verification:
(29 + 344 + 119) / 3 = 492 / 3 ≈ 164
This solution is correct!
Solution 4:
81, 105, 306
Verification:
(81 + 105 + 306) / 3 = 492 / 3 ≈ 164
This solution is correct!
Solution 5:
85, 221, 186
Verification:
(85 + 221 + 186) / 3 = 492 / 3 ≈ 164
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 492 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.