To determine the minimum score you need on the fourth test to get a B in the course, we need to calculate what total score will give you an average of at least 80%.

Step-by-Step Solution:

1. Total Possible Points:

   • The first three tests are 100 points each, so: $3 \times 100 = 300 \text{ points}$
   • The fourth test is 200 points.
   • Total points for all four tests: $300 + 200 = 500 \text{ points}$

2. Required Total Points for a B:

   • To achieve an 80% average, you need: $80\% \text{ of } 500 = 0.8 \times 500 = 400 \text{ points}$
   • You must score at least 400 points in total from all four tests.

3. Points Scored on First Three Tests:

   • Your scores on the first three tests were 77, 73, and 82. So, your total score so far is: $77 + 73 + 82 = 232 \text{ points}$

4. Points Needed on the Fourth Test:

   • To get at least 400 points in total, the minimum score you need on the fourth test is: $400 - 232 = 168 \text{ points}$

Thus, you need to score at least 168 points on the fourth test (which is out of 200) to get a B in the course.

Would you like further details or clarification on any part of the solution?

Here are 5 related questions to explore:

1. How would the required score change if the fourth test was worth 150 points instead of 200?
2. What would your average be if you scored exactly 168 on the fourth test?
3. What if your goal was an A (90%)—how much would you need to score on the fourth test?
4. How does changing the weight of the fourth test impact the overall average?
5. What if your scores were 70, 80, and 90 on the first three tests—how would this change the required score on the fourth test?

Tip: Always check the weight of each exam when calculating averages for courses with different test values.