What three numbers have an average of 166?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 166. This means if we add these three numbers together and divide by 3, we should get 166.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 166 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 166 * 3 = x + y + z
- So, the sum of our three numbers should be: 498
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 498.
Solution 1:
166, 166, 166
Verification:
(166 + 166 + 166) / 3 = 498 / 3 ≈ 166
This solution is correct!
Solution 2:
166, 166, 166
Verification:
(166 + 166 + 166) / 3 = 498 / 3 ≈ 166
This solution is correct!
Solution 3:
67, 331, 100
Verification:
(67 + 331 + 100) / 3 = 498 / 3 ≈ 166
This solution is correct!
Solution 4:
319, 115, 64
Verification:
(319 + 115 + 64) / 3 = 498 / 3 ≈ 166
This solution is correct!
Solution 5:
443, 14, 41
Verification:
(443 + 14 + 41) / 3 = 498 / 3 ≈ 166
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 498 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.