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Question
To receive grade 'A' in a course, one must obtain an average of 90 marks or more in five papers each of 100 marks. If Shikha scored 87, 95, 92 and 94 marks in first four paper, find the minimum marks that she must score in the last paper to get grade 'A' in the course.
Solution
Let x be the minimum marks scored in the last paper.
\[\text{ Then }, 90 \leq \frac{87 + 95 + 92 + 94 + x}{5} \leq 100\]
\[ \Rightarrow 90 \leq \frac{368 + x}{5} \leq 100\]
\[ \Rightarrow 450 \leq 368 + x \leq 500\]
\[ \Rightarrow 450 - 368 \leq 368 + x - 368 \leq 500 - 368\]
\[ \Rightarrow 82 \leq x \leq 132\]
\[\text{ But x can not be more than } 100\]
\[ \Rightarrow 82 \leq x \leq 100\]
\[\text{ Hence, the minimum marks that Shikha must score in the fifth paper is }82 .\]
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