Question 1199345
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        In this my post,  I will respond your question A, only.


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


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;A < f(x) > B


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


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Below is my correct solution.


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



<pre>
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).
</pre>

Solved, answered and explained.