BTGmoderatorDC wrote:Thabo owns exactly 140 books, and each book is either paperback fiction, paperback nonfiction, or hardcover nonfiction. If he owns 20 more paperback nonfiction books than hardcover nonfiction books, and twice as many paperback fiction books as paperback nonfiction books, how many hardcover books nonfiction books does Thabo own?
A) 10
B) 20
C) 30
D) 40
E) 50
OA B
Source: Official Guide
We are given that Thabo owns exactly 140 books, and each book is either paperback fiction, paperback nonfiction, or hardcover nonfiction.
We can let f = the number of paperback fiction books, n = the number of paperback nonfiction books, and h = the number of hardcover nonfiction books.
Since Thabo has 140 books, we have:
f + n + h = 140
We are also given that Thabo owns 20 more paperback nonfiction books than hardcover nonfiction books and twice as many paperback fiction books as paperback nonfiction books. Thus, we can say:
n = 20 + h
AND
f = 2n
We need to determine how many hardcover nonfiction books Thabo owns.
Since we have the variable n in each equation, we should express each variable in terms of n.
h = n - 20 and f = 2n
Finally, we can substitute (n - 20) for h and 2n for f in the equation f + n + h = 140, so we have:
2n + n + n - 20 = 140
4n = 160
n = 40
Thus, Thabo owns 40 - 20 = 20 hardcover nonfiction books.
Answer: B
