# Mathematiczz (The Problem Solving)

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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?

<<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
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?

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