A girl kept every doll she had receive since she was a baby. Later, however, she decided to get rid of most of them. She discarded 1/3 of the collection. Then, she gave 2/3 of the remaining dolls to a little girl who lived nearby. The rest of the dolls, the very best ones, she kept. There were 12 of these. How many dolls did she have in her collection?

Question

A girl kept every doll she had receive since she was a baby. Later, however, she decided to get rid of most of them. She discarded 1/3 of the collection. Then, she gave 2/3 of the remaining dolls to a little girl who lived nearby. The rest of the dolls, the very best ones, she kept. There were 12 of these. How many dolls did she have in her collection?

Please help me!!!!! I am drowning in this problem!!!!

<<A girl kept every doll she had receive since she was a baby. Later, however, she decided to get rid of most of them. She discarded 1/3 of the collection. Then, she gave 2/3 of the remaining dolls to a little girl who lived nearby. The rest of the dolls, the very best ones, she kept. There were 12 of these. How many dolls did she have in her collection?>>

Is this what she kept?
2/3*1/3 of the original collection
Should the problem read then..
Later, however, she decided to get rid of most of them. She kept 2/3 of the collection. Then, she kept 1/3 of the remaining dolls

Sometimes you have to reread problems to see what they mean...

A girl kept every doll she had receive since she was a baby. Later, however, she decided to get rid of most of them. She discarded 1/3 of the collection. Then, she gave 2/3 of the remaining dolls to a little girl who lived nearby. The rest of the dolls, the very best ones, she kept. There were 12 of these. How many dolls did she have in her collection? <This is the correct question.> (Are you sure of your answer?)

Let d represent the number of dolls in her collection. We're told she gave away 1/3 of the d so she has (2/3)d remaining. She then gave away (2/3)*(2/3)d, two-thirds of the remaining amount, so she still has (1/3)(2/3)d.
We're then told that
(1/3)(2/3)d=12
Can you figure out d from this equation?

Answer 1

Sure! To find the value of d, we can solve the equation (1/3)(2/3)d = 12.

To solve for d, we need to isolate it on one side of the equation. We can start by multiplying both sides of the equation by (3/2) to get rid of the fraction:

(3/2) * (1/3)(2/3)d = (3/2) * 12

Simplifying the left side of the equation:

d = (3/2) * 12

d = 36/2

d = 18

So, she had 18 dolls in her collection.