Question

Rita earns scores of 83, 87, 85, 88, and 90 on her five chapter tests for a certain class and a grade of 82 on the class project.

The overall average for the course is computed as follows: the average of the five chapter tests makes up 30% of the course
grade; the project accounts for 30% of the grade; and the final exam accounts for 40%. 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

Given:

Rita earns scores of 83, 87, 85, 88, and 90 on her five-chapter tests for a certain class.

And a grade of 82 on the class project.

First, we will find the average of the scores of the five tests

`5-tests\text{ }average=(83+87+85+88+90)/(5)=(433)/(5)=86.6`

The overall average for the course is computed as follows:

30% of the course grade ⇒ Rita get 86.6

30% of project grade ⇒ Rita get 82

40% of the final exam ⇒ let Rita get x

We will find the value of x provided that Rita will earn a "B" score

a "B" is an overall score greater than or equal to 80, but less than 90

So, we will find (x) as follows:

`(30*86.6+30*82+40*x)/(100)\ge80`

Solve the inequality to find (x):

`\begin{gathered} 5058+40x\ge8000 \\ 40x\ge8000-5058 \\ 40x\ge2942 \\ x\ge(2942)/(40) \\ \\ x\ge73.55 \end{gathered}`

And the upper limit will be as follows:

`(30*86.6+30*82+40x)/(100)<90`

Solve to find (x):

`\begin{gathered} 5058+40x<9000 \\ 40x<9000-5058 \\ 40x<3942 \\ x<(3942)/(40) \\ \\ x<98.55 \end{gathered}`

So, the answer will be:

To obtain a "B", Rita needs to score between 73.55 and 98.55