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First, we will assume that Alice and Julie start with x number of pens and as given in question Alive gives 16 of her pens to Julie. Therefore, Alice has (x−16) pens and Julie has (x+16) pens. And finally make one variable equation by using the condition that Julie has two times as many pens as Alice does after giving 16 of her pens to Julie.

Let Alice and Julie start with x number of pens.

When Alice gives 16 pens to Julie

Then Alice has (x−16) pens

and Julie has (x+16).

Now, according to the question-

$ \Rightarrow $ x+16= $ 2\left( {x - 16} \right) $

$ \Rightarrow $ x+16=2x−32

$ \Rightarrow $ 2x−x=32+16

$ \Rightarrow $ x=48

Hence, Alice and Julie both had 48 pens at the start.