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 equalled 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?

Hithispatato Aug 22, 2018

#1**+2 **

H = hardcover books

Paperback books = twice the harcover books = 2H

Original number in the collection = H + 2H = 3H

Books checked out = H + x(3H/9) where x is the number of members checking out the paperback books

Paperbacks returned = 2(3H /9)

Paperbacks not returned = (x - 2)(3H/9)

So we have this equation

Books in collection = [ books returned ] + [ books not returned ]

3H = [2 (3H/9)] + [ H + (x - 2)(3H/9) ] simplify

3H = [ H(2/3) ] + [ H + (H)(x - 2)/3 ] divide through by H

3 = (2/3) + 1 + (x - 2)/3

3 = (2/3) + 1 + (x - 2)/3 multiply through by 3

9 = 2 + 3 + x - 2

9 = 3 + x

9 - 3 = x

6 = x

You need to make 5 calls.....one to Member 7427 and (x - 2) = (6 - 2) = 4 more to those who checked out the unreturned paperbacks

CPhill Aug 22, 2018