How many of each book ?

Question

The library has 750 books . there are three times as many science fiction as fantasy , two times as many mystery as fantasy and four times as many biographies as fantasy , how many of each book ?

Answer 1

The total number of books are given (750) in terms of the number of fantasy books (let's call that number f).

Number of fantasy books = f

Number of science fiction books = 3f

Number of mystery books = 2f

Number of biographies = 4f

f + 3f + 2f + 4f = 10f = total number of books

We know that the total number of books is 750, so 10f = 750 and 10f/10 = 750/10, which means f = 75. So the total number in each genre are:

Number of fantasy books = f = 75

Number of science fiction books = 3f = 3*75 = 225

Number of mystery books = 2f = 2*75 = 150

Number of biographies = 4f = 4*75 = 300

So there are 75 fantasy books, 225 science fiction books, 150 mystery books, and 300 biographies.

Answer 2

Okay! Same concept as Pallavi G. explained above; I just took a slightly different route to get there. Warning, mine might be a little wordier, but that's how I got to the answer, so many someone else will think this way too! :)

We have 750 books total. We know that there are 3x as many Science Fiction (we'll call this SF) as Fantasy (which we'll call FA). There are 2 times as many Mystery (M) as Fantasy, and there are 4 times as many Biography (we'll call this B) as F.

So, more concisely, and mathematically:

SF = 3FA (the # of Science Fiction books is equal to 3x the # of Fantasy books)

M = 2FA (the # of Mystery books is equal to 2x the # of Fantasy books)

B = 4FA (the # of Biography books is equal to 4x the # of Fantasy books)

First, I noticed that since everything is in multiples of FA's, if I find out how many FA's there are, I can deduce how many of each other type of book there are!

Well, we know one FA book is equal to, well, one FA book. What I did was add up all the FA's that made up the three other book types. So, 3+2+4=9. So in those 3 types of books you have 9 FA's. And in one FA you have one FA. So how many FA's total in the library? 9+1=10!

To figure out how many FA books we have, I divided 750 by 10, which luckily is a nice easy and clean multiple of 10 equation. 750/10=75. So, we have:

75 FA books

75x3=225 SF books

75x2=150 M books

75x4=300 B books

75 Fantasy, 225 Science Fantasy, 150 Mystery, and 300 Biography.

They're each a multiple of 10, or a multiple of a "SciFi book!"

Thanks for reading!