Question

Rita earns scores of 70, 76, 86, 87, and 85 on her five chapter tests for a certain class and a grade of 85 on the dass project.

The overall average for the course is computed as follows: the average of the five chapter tests makes up 60% of the course
grade; the project accounts for 10% of the grade; and the final exam accounts for 30%. What scores can Rita earn on the final
exam to earn a "B" in the course if the cut-off for a "B" is an overall score greater than or equal to 80, but less than 90? Assume
that 100 is the highest score that can be earned on the final exam and that only whole-number scores are given.
To obtain a "B", Rita needs to score between and inclusive.

Answer 1

To obtain a "B", Rita needs to score between 76.7 and 100.

Explanation:

Chapter tests mean:

`M = (70 + 76 + 86 + 87 + 85)/(5) = 80.8`

Grades:

80.8 worth 60% = 0.6

85 worth 10% = 0.1

x worth 0.3.

So her grade is:

`G = 80.8*0.6 + 85*0.1 + 0.3x = 56.98 + 0.3x`

What scores can Rita earn on the final exam to earn a "B" in the course if the cut-off for a "B" is an overall score greater than or equal to 80, but less than 90?

G has to be greater than or equal to 80 and less than 90, so:

`80 \leq G < 90`

Lower bound:

`G \geq 80`

`56.98 + 0.3x \geq 80`

`0.3x \geq 80 - 56.98`

`x \geq (80 - 56.98)/(0.3)`

`x \geq 76.7`

Upper bound:

`G < 90`

`56.98 + 0.3x < 80`

`0.3x < 90 - 56.98`

`x < (90 - 56.98)/(0.3)`

`x < 110`

Highest grade is 100, so:

To obtain a "B", Rita needs to score between 76.7 and 100.