Question

Alice and Julie start with the same number of pens. After Alive gives 16 of her pens to Julie, Julie then has two times as many pens as Alice does. How many pens did Alice have at the start?

Answer 1

Hint: To solve this question we use the basic one variable equation, so that we easily solve and get the answer. 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.

Complete step-by-step answer:
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.

Note: Equation is a convenient way to represent conditions or relations between two or more quantities. For example, if Alice having ‘x’ pen, then after giving ‘n’ pen to the Julie, then Alice having number of pens = $ \left( {x - n} \right) $ . similarly, after taking n pens from Alice, Julie having $ \left( {x + n} \right) $ pens.