Final answer:
The student needs at least 90 points on the fourth test, which is worth 200 points, to achieve a B in the course, as this would lead to an average of 80% across all four tests.
Step-by-step explanation:
To determine the minimum score needed on the fourth test to get a B in the course, which requires an average of at least 80 percent, we can calculate the total points currently earned and then find out how many points are needed on the final test to reach the average.
- First, we sum the points from the first three tests: 72 + 84 + 74 = 230 points.
- Since the fourth test is worth double, we multiply the desired average score, 80%, by the total possible points (400 points, from the 3 tests worth 100 points each plus the fourth test worth 200 points): 0.80 x 400 = 320 points needed in total.
- To determine the points needed on the fourth test, subtract the points already earned from the total needed: 320 - 230 = 90 points.
- Finally, because the fourth test is worth 200 points, we calculate the percentage needed: 90 / 200 = 0.45, which means 45% of 200 points is needed on the final test.
Therefore, to achieve a B in the course, the student needs at least 90 points out of 200 on the fourth test, which corresponds to a percentage score of 45%.