lara arranged the books in her bookshelf by size. 2/10 of the books were tall and 1/2 of the books were medeium sized. If 12 of the books were small, how manyu total books did she arrange?
2/10 + 5/10 = 7/10
(3/10)x = 12
x = 12/(3/10)
x = 12 * (10/3)
x = 120/3
x = ?
could you please explain how you got 5/10 and 3/10?
1/2 = 5/10
10/10 - 7/10 = 3/10
To find the total number of books that Lara arranged on her bookshelf, we need to determine the number of tall and medium-sized books.
Let's say the total number of books is represented by "x".
From the given information, we know that 2/10 of the books were tall, which can be written as (2/10) * x. Similarly, 1/2 of the books were medium-sized, which can be written as (1/2) * x.
We are also given that 12 books were small.
Now, we can set up an equation to solve for "x":
(2/10) * x + (1/2) * x + 12 = x
To simplify the equation, we need to get rid of the fractions. We can do this by multiplying each term by the least common multiple (LCM) of the denominators, which is 10 in this case:
(2/10) * 10x + (1/2) * 10x + 12 * 10 = 10x
Now the equation becomes:
2x + 5x + 120 = 10x
Combining like terms:
7x + 120 = 10x
Moving all the terms with "x" to one side of the equation:
10x - 7x = 120
3x = 120
Dividing both sides of the equation by 3:
x = 40
Therefore, Lara arranged a total of 40 books on her bookshelf.