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A student's grade in a course is the

A student's grade in a course is the average of 4 test grades and a final exam that is worth twice as much as each test. Suppose a student has test grades of 91, 82, 83, and 92. Write an equation to model this situation where x is the student's grade on the final exam and y is the student's average for the course.Then find the score they will need to receive on their final exam if they want to have a grade of 90 for the course.

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5 Answers

Hi, Renetta.

As Jessica said, the equation for average is the sum of all the test scores divided by the number of tests. However, the question says that the final grade counts twice as much as each test. The final grade is the unknown, x, but it counts twice in the course average so we add 2x. Also, since it counts as 2 tests, we divide by 6.

So your equation would be:

(91 + 82 + 83 + 92 + 2x) / 6 = 90        

(348 + 2x) / 6 = 90                 Simplify

348 + 2x = 540                      Multiply both sides by 6

2x = 192                               Subtract 348 from both sides

x = 96                                   Divide both sides by 2

So the student will need to get a 96 on the final to get a 90 in the course.

 

Use weighing concepts.

You weigh 1 for each test, and 2 for the final. So, the average score should be

(1*91 + 1*82 + 1*83 + 1*92 + 2x)/(1+1+1+1+2)

Simplifying it gives you the answer.

To summarize the answers below, the equation that would model this situation would be:

      y = (91 + 82 + 83 + 92 + 2x) / 6 = (348 + 2x) / 6

                                                      = [2*(174 + x)] / 6 = (174 + x) / 3

      y= (348+ 2x) / 6     OR     y = (174 + x) / 3


Then you would plug in 90 for y in either equation to solve for x which, as was stated below, is equal to 96.

The equation for average is:

The sum of all the test scores/the number of tests.

For this case we know that the test scores are 91, 82, 83, 92 and some unknown x

From this we know the total number of tests is 5 so the equation looks something like

(91+82+83+92+x)/5

the average of the tests in this case equals y so the equation is

[(91+82+83+92+x)/5]=y

You want to have a grade (or average) or 90 for the class so y=90

[(91+82+83+92+x)/5]=90

To solve first multiply both sides by 5, then subtract (91+82+83+92) to leave x on one side and the answer on the other.

Comments

Jessica, Your explanation is great, but you overlooked that the final exam counted as 2 test grades, not just one. So you would need to use 2x in the equation, and divide the sum by 6.

Comment

The first thing that you will want to do is write the equation

91+82+83+92+x=y in this x represents the final exam and y is the final average

since th final average is given to us as 90 the easiest way to find out what the final exam score is now is to multiply 90 x 5= 450 this gives us the total that the 5 scores will need to be in order to have an average of 90 then substitute the 450 for y in the formula

91+82+83+92+x=450 we then take the total of the four given numbers and subtract it from the 450 in order to solve for x

450-348=102 therefore x=102 then substitute the 102 for x and check your answer

91+82+83+92+102=450

450 / 5 = 90 I hope this helps