Total number of books = 36
Let the number of library books be = x
Let the number of textbooks be = y
Let the number of free reading books be = z
[tex]x+y+z=36[/tex] ..... (1)
As mentioned, number of library books and the free reading books combined equals twice the number of textbooks, equation is [tex]x+z=2y[/tex] Â .......(2)
The number of textbooks and free reading books combined equals three times the number of library books, equation is [tex]y+z=3x[/tex] ... (3)
Putting the value of x+z from equation (2) in (1)
[tex]y+2y=36[/tex]
[tex]3y=36[/tex]
[tex]y=12[/tex]
Putting the value of y+z from equation (3) in (1)
[tex]x+3x=36[/tex]
[tex]4x=36[/tex]
[tex]x=9[/tex]
As, [tex]x+y+z=36[/tex]
[tex]9+12+z=36[/tex]
[tex]z=15[/tex]
Hence, Grant has 9 library books, 12 textbooks and 15 free reading books.
