SOLUTION: Hi 80 percent of the books in a box are 2nd hand books and the rest are new. 10 percent of the new and 60 percent of the 2nd hand are english and the rest are chinese. After anoth

Let E be the number of English books and C be the number of Chinese books.

Let S be the number of the second hand books and N be the number of new books.


Then   =  = 4, since  "80 percent of the books in a box are 2nd hand books and the rest are new."

In other words,  S = 4N.     (1)


Next, the condition says that

0.1*N + 0.6*S = E       (2)   ("10 percent of the new and 60 percent of the 2nd hand are english")   and

0.9*N + 0.4*S = C       (3)   ("the rest are chinese")


Now, substitute (1) into (2) and (3). You will get

0.1*N + 0.6*(4N) = E    (2')

0.9*N + 0.4*(4N) = C    (3')

or, simplifying


2.5*N = E                (2'')

2.5*N = C                (3'')


Thus  E = C   (!!!).


Next, use the last condition  

 = ,

which (due to (!!!) ) is the same as

 = .


It implies  2*(E+15) = 3E,   or  2E + 30 = 3E  ====>  E = 30.


Thus the number of English books initially was 30.  


Then the total number of the books at the end is  E + C + 15 = E + E + 15 = 75.