Lara arranged the books in her bookshelf by size she arranged 2/10 of the books were tall and 1/2 of the books were medium sized. if 12 of the books were small, how many total books did she arrange?
x = 2/10 x + 1/2 x + 12
6/20 x = 12
x = 40
To find the total number of books Lara arranged, we need to determine the fraction of books that are tall and medium-sized. First, let's find the fraction of books that are tall.
Since Lara arranged 2/10 of the books as tall, this means 2/10 represents the fraction of tall books. To simplify this fraction, we can divide the numerator and denominator by their greatest common divisor, which is 2. So, 2/10 simplifies to 1/5.
Now, let's find the fraction of books that are medium-sized. Lara arranged 1/2 of the books as medium-sized, which doesn't require any simplification.
Next, let's add the fractions of tall and medium-sized books together to find the total fraction of those two sizes: 1/5 + 1/2.
To add fractions, we need a common denominator. In this case, the common denominator is 10. So the sum of the fractions becomes (1/5) + (5/10) = (2/10) + (5/10) = 7/10.
This means 7/10 of the total books Lara arranged are either tall or medium-sized. Now, we can set up a proportion to find the total number of books.
Since 7/10 represents the fraction of tall and medium-sized books, this fraction should be equal to the fraction of small books (12 books out of the total number of books). Using a proportion, we have:
(7/10) = (12/total number of books)
To solve for the total number of books, we can cross-multiply and then divide:
7 * total number of books = 10 * 12
7 * total number of books = 120
Dividing both sides by 7:
total number of books = 120 / 7
The total number of books Lara arranged is approximately 17 books.