Please solve the following problem with the steps PLEASE NOT

Please solve the following problem with the steps: (PLEASE NOTE THAT \'GP\' STANDS FOR GRADED PROBLEM IN LINEAR ALGEBRA COURSE)

2. (10 points) Suppose you are teaching this course instead of me and trying to come up with a thought- ful/meaningful/fun/not too easy/not too difficult question for the GPs. What sort of question would you ask your students and why? After coming up with the question, solve it! (Correctly, of course O)

Solution

Question:- In a certain Algebra class there is a total of 350 possible points. These points come from 5 homework sets that are worth 10 points each and 3 hour exams that are worth 100 points each. A student has received homework scores of 4, 8, 7, 7, and 9 and the first two exam scores are 78 and 83. Assuming that grades are assigned according to the standard scale and there are no weights assigned to any of the grades is it possible for the student to receive an A in the class and if so what is the minimum score on the third exam that will give an A? What about a B?

Solution:-

Okay, let’s start off by defining p to be the minimum required score on the third exam.

Now, let’s recall how grades are set. Since there are no weights or anything on the grades, the grade will be set by first computing the following percentage.

Actual point/Total possible points = Grade Percentage

Since we are using the standard scale if the grade percentage is 0.9 or higher the student will get an A. Likewise if the grade percentage is between 0.8 and 0.9 the student will get a B.

We know that the total possible points is 350 and the student has a total points (including the third exam) of,

4+8+7+7+9+78+83+p = 196+p

The smallest possible percentage for an A is 0.9 and so if  p is the minimum required score on the third exam for an A we will have the following equation.

196+p/350 = 0.9

This is a linear equation that we will need to solve for p.

196+p = 0.9(350) = 315

So, the minimum required score on the third exam is 119. This is a problem since the exam is worth only 100 points. In other words, the student will not be getting an A in the Algebra class.

Now let’s check if the student will get a B. In this case the minimum percentage is 0.8. So, to find the minimum required score on the third exam for a B we will need to solve,

196+p/350 = 0.8

Solving this for p gives,

196+p = 0.8(350) =280

p = 280-196 = 84

So, it is possible for the student to get a B in the class. All that the student will need to do is get at least an 84 on the third exam.