ABC Bookstore sells packages of books that include both new and used books. New books cost $20 and used books cost $8. The bookstore wants to sell packages that have 36 books total, and the store charges $456 for each package. How many new and used books will be in each Package?

There are 14 new books and 22 old books in the package.

Step-by-step explanation:

New books cost $20 and used books cost $8. The bookstore wants to sell packages that have 36 books total, and the store charges $456 for each package.

If the number of new books in the package is x and that of old books in the package is y, then we can write two simultaneous equations as

x + y = 36 ... (1) and

20x + 8y = 456

⇒ 5x + 2y = 114 ... (2)

Now, solving equations (1) and (2) we get,

5x + 2 (36 - x) = 114

⇒ 3x + 72 = 114

⇒ 3x = 42

⇒ x = 14

Then, y = 36 - x = 22.

Therefore, there are 14 new books and 22 old books in the package. (Answer)