SOLUTION: In your Economics 101 class, you have scores of 68,82, 87, and 89 on the first 4 of 5 tests. To get a grade of B, the average of the first five test scores must be greater than or

Question 1199345: In your Economics 101 class, you have scores of 68,82, 87, and 89 on the first 4 of 5 tests. To get a grade of B, the average of the first five test scores must be greater than or equal to 80 and less than 90.
A. Solve the inequality to find the range of the score that you need on the last test to get a B.
B. What score do you need if the fifth test counts double?

Part A Set-up:
90 < (68 + 82 + 87 + 89 + x)/5 >= 80

90 < (326 + x)/5 >= 80

90(5) < (326 + x) >= 80(5)

450 < 326 + x >= 400

450 - 326 < x >= 400 - 326

124 < x >= 74

Let R = range of the score needed on last test x.

R = 74 <= x < 124

1. Is my work for Part A right?
2. What is the set-up for Part B.
Answer by ikleyn(52803)   (Show Source): You can put this solution on YOUR website!
.

        In this my post, I will respond your question A, only.

        Your solution is INCORRECT, since you use incorrect notations of the form

                A < f(x) > B

        everywhere in your post. The right form of a compound inequality is   A < f(x) < B   (watch carefully for the inequality signs ( ! ) ).

        Below is my correct solution.

        Also, note that the scores greater than 100 are not in use in such situation/context.

80 < (68 + 82 + 87 + 89 + x)/5 <= 90


80 < (326 + x)/5 <= 90


80(5) < (326 + x) <= 90(5)


400 < 326 + x <= 450


400 - 326 < x <= 450 - 326


74 < x <= 124


Let R = range of the score needed on last test x.


R = { 74 < x <= 100 }   (I use 100 as the maximal possible score which is in use).

Solved, answered and explained.

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