AbdurRakib 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
OG 2017 New Question
We are asked about the hardcover, non-fiction, so it makes sense to use X
to indicate the element about which we were asked. So let's just call that one X.
If they tell me that there are 20 more paperback, non-fiction than these, well
this is a verbal sentence establishing the ratio of two or more sizes, I need to add to the
smaller quantity. That there are 20 more of these, than these, that means that this
quantity is greater; so this quantity is going to be equal to this quantity +20.
So I added to the small one 20, in order to make it equal to the bigger one.
Same thing here; there are twice as many paperback fiction as paperback non-fiction.
Paperback nonfiction, I know it's X + 20; there are twice as
many these as these, in other words this larger
quantity is going to be equal twice the smaller quantity. At the end of the day, I
know that 2(X + 20) plus this quantity, which is X + 20 plus
the original quantity, which we referred to as an X, equals a 140. This is one
equation with one unknown; should be solvable. 2X + 40 + X + 20 + X =140.
...
4X = 80, so that means that X is equal to a 20 the correct answer is B.