Question

Help: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

Answer 1

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 2

*sigh*

Answer 3

call the number of hard cover x
and the number of paperback as 2x (twice as many as hardcover)
total number of books is x+2x = 3x

Answer 4

the "group" checked out all the paperbacks

Each took one ninth of our original collection.
that means each took 1/9 of 3x or 3x/9 or x/3
call the number in the group N

then
N * number of books per person = total number of paperbacks
\[ N \cdot \frac{x}{3} = 2x \]
solve for N (multiply both sides by 3/x)
you get
N= 6 (people who took out paperbacks)

Answer 5

Two of those members brought their books back

that means N-2 = 6-2 = 4 people are late
plus the one who took the hardcovers, means

you call 5 people

Answer 6

Yep that's correct. Thanks.