Question

Marjorie needs to earn a C in her Geology class. Her current test scores are 71,77, and 72. Her final exam is worth 6 test scores. In order to earn a C, Marjorie’s average must lie between 70 and 79 inclusive. What range of scores can Marjorie receive on the final exam to earn a C in the course?

Answer 1

68 to 82 Points.

Explanation:

To find the range of scores that Marjorie needs to have to stay in the 70 to 79 range we first need to define the variables that we need to find.

Let x = Score that Marjorie needs

Since the exam is worth 6 exams, we will then use 6x to denote the weight of the final exam.

Now we need to add all the other exams and divide it to the number of exams.

`(6x + 71 + 77 + 72)/(9)`

`(6x + 220)/(9)`

Now let's look for the score that Marjorie needs to get a 70 average.

`(6x + 220)/(9)=70`

We begin by multiplying both sides by 9 to remove to begin solving for x.

`6x+220=(9)70`

`6x+220=630`

`6x=630-220`

`(6x)/(6) =(410)/(6)`

`x=68.33`

So the minimum score that Marjorie needs is 68.

Now let's look for the score that Marjorie needs to get to a 79 average.

We still use the same values except the average.

`(6x + 220)/(9)=79`

We begin by multiplying both sides by 9 to remove to begin solving for x.

`6x+220=(9)79`

`6x+220=711`

`6x=711-220`

`(6x)/(6) =(491)/(6)`

`x=81.83` or {tex}82[/tex]

So the range of scores that Marjorie needs to get an average of 70 to 79 is 68 to 82 Points.