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Chapter 10: Problem 6

On Monday, 40 of the 160 available books in a library's collection were borrowed. On Tuesday, half of the books borrowed on Monday were returned and on Wednesday half of the remaining borrowed books from Monday were returned. On Thursday, the library receives 30 more available books, and a sixth of the remaining borrowed books from Monday are returned. On Friday, 30 more books are borrowed and on Saturday 35 more books are borrowed. If no other books were borrowed, returned, or received during the week, what is the percent change of the available books at the end of the day Monday to the available books at the end of the day on Saturday?

Short Answer

Expert verified
The percent change of the available books at the end of the day Monday to the available books at the end of the day on Saturday is -1.67%.

Step by step solution

01

Calculate Borrowed Books

On Monday, 40 out of 160 books were borrowed, leaving 120 books available. On Tuesday, half of the books borrowed on Monday were returned, so 20 books were returned. On Wednesday, half of the remaining borrowed books from Monday were returned, so 10 more books were returned. On Thursday, a sixth of the remaining borrowed books from Monday were returned, which is approximately 3.33, however, since we can't have part of a book, we consider it as 3 books were returned.
02

Calculate Books added

On Thursday the library receives 30 new books and so the total number of books on Thursday becomes 120 + 20 + 10 + 3 (available books and the returned books from Monday to Thursday) + 30 (added books on Thursday) = 183. On Friday, 30 more books are borrowed, so the available books on Friday would be 183 - 30 = 153. Finally, on Saturday 35 additional books are borrowed, so available books on Saturday would be 153 - 35 = 118.
03

Calculate Percentage Change

We are asked to find the percent change of the available books from Monday to Saturday. The formula for percent change is: \[ Percent Change = \frac{(Final Value - Initial Value)}{Initial Value} * 100\% \] Substituting the given values into the formula gives \[ Percent Change = \frac{(118 - 120)}{120} * 100\% = -1.67\% \]

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