What three numbers have an average of 158?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 158. This means if we add these three numbers together and divide by 3, we should get 158.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 158 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 158 * 3 = x + y + z
- So, the sum of our three numbers should be: 474
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 474.
Solution 1:
158, 158, 158
Verification:
(158 + 158 + 158) / 3 = 474 / 3 ≈ 158
This solution is correct!
Solution 2:
158, 158, 158
Verification:
(158 + 158 + 158) / 3 = 474 / 3 ≈ 158
This solution is correct!
Solution 3:
130, 242, 102
Verification:
(130 + 242 + 102) / 3 = 474 / 3 ≈ 158
This solution is correct!
Solution 4:
26, 305, 143
Verification:
(26 + 305 + 143) / 3 = 474 / 3 ≈ 158
This solution is correct!
Solution 5:
239, 173, 62
Verification:
(239 + 173 + 62) / 3 = 474 / 3 ≈ 158
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 474 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.