Question

the public library where i work originally had one hardcover and two paperback copies of every book that sir arthur conan doyle ever wrote. the records for the month of march show that member $7427$ checked out all of the hardcover conan doyle books and never brought them back. the following month, a group of other members checked out every conan doyle book left in the library building. each of those members took the same number of books, and that number equaled one ninth of our original collection. two of those members brought their books back on time. it's my job to call the other people who checked out conan doyle books, including member $7427$, and demand the return of their overdue items. how many angry phone calls do i have to make?

Answer 1

The number of angry phone calls you have to make is equal to the number of remaining members who checked out books.

Step-by-step explanation:

The library originally had one hardcover and two paperback copies of every book Sir Arthur Conan Doyle ever wrote. In March, member 7427 checked out all of the hardcover Conan Doyle books and never returned them.

The following month, a group of members checked out the remaining Conan Doyle books, with each member taking one-ninth of the original collection.

Two members returned their books on time, so the number of angry phone calls you have to make is equal to the number of remaining members who checked out books.

To find the number of remaining members, we first need to determine the original collection size. If member 7427 checked out all the hardcover books, this means there were originally two paperback copies of each book, giving a total of 2 hardcover books + 4 paperback books = 6 books.

Since each member took one-ninth of the original collection, we can divide 6 books by 9 to find the number of books each member took.

This gives us 6/9 = 2/3 of a book per member.

Since two members returned their books on time, the number of remaining members is the total number of members minus the two who returned their books, which is 3 - 2 = 1 member.

Therefore, you only need to make one angry phone call to member 7427 to demand the return of their overdue books.