What three numbers have an average of 167?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 167. This means if we add these three numbers together and divide by 3, we should get 167.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 167 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 167 * 3 = x + y + z
- So, the sum of our three numbers should be: 501
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 501.
Solution 1:
167, 167, 167
Verification:
(167 + 167 + 167) / 3 = 501 / 3 ≈ 167
This solution is correct!
Solution 2:
167, 167, 167
Verification:
(167 + 167 + 167) / 3 = 501 / 3 ≈ 167
This solution is correct!
Solution 3:
186, 73, 242
Verification:
(186 + 73 + 242) / 3 = 501 / 3 ≈ 167
This solution is correct!
Solution 4:
9, 331, 161
Verification:
(9 + 331 + 161) / 3 = 501 / 3 ≈ 167
This solution is correct!
Solution 5:
440, 55, 6
Verification:
(440 + 55 + 6) / 3 = 501 / 3 ≈ 167
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 501 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.