SOLUTION: A student's grade in a course is the average of 4 test grades and a final exam that is worth four times as much as each test. Suppose a student has test grades of 89, 90, 86, and 9

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Question 763034: A student's grade in a course is the average of 4 test grades and a final exam that is worth four times as much as each test. Suppose a student has test grades of 89, 90, 86, and 91. Write an equation to model this situation where is the student's grade on the final exam and 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.
Final exam score needed

Answer by Stitch(470) About Me  (Show Source):
You can put this solution on YOUR website!
Let A = 1st Test
Let B = 2nd Test
Let C = 3rd Test
Let D = 4th Test
Let F = Final
Your equation would be:
%28A%2BB%2BC%2BD%2B4F%29%2F8+=+F
The eight comes from the 4 tests plus the final is worth 4 tests.
Plug the given test grades into the equation.
%2889%2B90%2B86%2B91%2B4F%29%2F8+=+F
Combine like terms.
%28356%2B4F%29%2F8+=+F
Multiply both sides by 8.
356+%2B+4F+=+8F
Subtract 4F from both sides.
356+=+4F
Divide both sides by 4.
highlight%2889+=+F%29
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Now find the score on the final to give the student a 90 for the course.
Our equation will now change a little bit. It will no longer be equal to F, we will set it eqaul to 90.
%28A%2BB%2BC%2BD%2B4F%29%2F8+=+90
Plug in the given test values.
%2889%2B90%2B86%2B91%2B4F%29%2F8+=+90
Combine like terms.
%28356%2B4F%29%2F8+=+90
Multiply both sides by 8.
356+%2B+4F+=+720
Subtract 356 from both sides.
4F+=+364
Divide both sides by 4.
highlight_green%28F+=+91%29