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At the start of a certain week, a school library had 100 comic books,
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20 Mar 2023, 10:54
20 Mar 2023, 10:54
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At the start of a certain week, a school library had 100 comic books, all of which were on the shelf on Monday morning. 25% of the comic books issued on Tuesday and 12.5% of the comic books issued on Wednesday were returned by Saturday morning. Books are issued only on Tuesdays and Wednesdays. Number of comic books issued on Wednesday were twice the number of comic books issued on Tuesday during that week. If there are atleast 40 comic books in the library that Saturday morning, what could be the greatest number of books that could be issued during that week?
24
48
72
80
90
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24
48
72
80
90
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Re: At the start of a certain week, a school library had 100 comic books,
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30 Mar 2023, 09:33
30 Mar 2023, 09:33
1
Expert Reply
To find the maximum number of comic books issued during the week, we need to maximize the number of comic books that were not returned by Saturday morning. Let x be the number of comic books issued on Tuesday. Then, the number of comic books issued on Wednesday is 2x.
On Tuesday, 25% of the comic books issued were returned, so 75% were not returned. On Wednesday, 12.5% of the comic books issued were returned, so 87.5% were not returned. Therefore, the total number of comic books that were not returned by Saturday morning is:
100 + 0.75x + 0.875(2x) = 100 + 0.75x + 1.75x = 100 + 2.5x
We know that this number is at least 40, so:
100 + 2.5x >= 40
2.5x >= -60
x >= -24
Since x is the number of comic books issued on Tuesday, it must be a positive integer, so we take the smallest possible value of x that satisfies the inequality above, which is x = 24. Then, the number of comic books issued on Wednesday is 2x = 48.
Therefore, the maximum number of comic books issued during the week is 24 + 48 = 72. The correct answer is (C) 72.
On Tuesday, 25% of the comic books issued were returned, so 75% were not returned. On Wednesday, 12.5% of the comic books issued were returned, so 87.5% were not returned. Therefore, the total number of comic books that were not returned by Saturday morning is:
100 + 0.75x + 0.875(2x) = 100 + 0.75x + 1.75x = 100 + 2.5x
We know that this number is at least 40, so:
100 + 2.5x >= 40
2.5x >= -60
x >= -24
Since x is the number of comic books issued on Tuesday, it must be a positive integer, so we take the smallest possible value of x that satisfies the inequality above, which is x = 24. Then, the number of comic books issued on Wednesday is 2x = 48.
Therefore, the maximum number of comic books issued during the week is 24 + 48 = 72. The correct answer is (C) 72.
Re: At the start of a certain week, a school library had 100 comic books,
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28 Dec 2023, 06:57
28 Dec 2023, 06:57
Hello Could you please explain why are we adding 0.75x when we know that total number of books are only 100 . My thinking goes like If total number of books is 100 and certain percent of books are rented out then there must be remaining number of book which would be less than 100 so adding 0.75x confuses me a bit ,if you could please elaborate more on that
