Question

In a class in which the final course grade depends entirely on the average of four equally weighted 100-point tests, Lisa has scored 86, 89, and 85 on the first three. What range of scores on the fourth test will give Lisa a B for the semester (an average between 80 and 89, inclusive)? Assume that all test scores have a non-negative value. Express your answer in interval notation.

a) [80, 85)
b) [82, 88)
c) [84, 89)
d) [86, 90)

Answer 1

Lisa must score between 60 and 96 on her fourth test to maintain a B average for the semester. The range in interval notation is [60, 96]. None of the provided answer choices are correct.

Step-by-step explanation:

To determine the range of scores Lisa can receive on her fourth test to maintain a B average (between 80 and 89 inclusive), we need to calculate the total number of points she needs.

Lisa's scores on the first three tests are 86, 89, and 85. Therefore, the total points so far are:

86 + 89 + 85 = 260

Since the final course grade depends on the average of four tests, to achieve at least a B (80 average), she would need:

80 (average score) × 4 (number of tests) = 320 (total minimum points)

To find the minimum score needed on the fourth test:

320 (total minimum points) - 260 (current total points) = 60.

However, Lisa needs to maintain the average up to an 89 to stay in the B range. So to find the maximum score:

89 (average score) × 4 (number of tests) = 356 (total maximum points)

To find the maximum score possible on the fourth test:

356 (total maximum points) - 260 (current total points) = 96.

Therefore, the range of scores that Lisa could receive on the fourth test to maintain a B for the semester is between 60 and 96.

In interval notation, this is expressed as:

[60, 96]

None of the answer choices provided, i.e., a) [80, 85), b) [82, 88), c) [84, 89), d) [86, 90), match the correct range.