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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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.

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.

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

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