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A dealer packed 290 pens into six boxes of different colors - yellow, blue, black, green, red, and pink. There are as many pens in the blue and yellow boxes combined as there are in the pink box. There are one and a half times pens in the pink box as there are in the yellow box. There are twice as many pens in the black box as there are in the yellow box. There are twice as many pens in the red box as there are in the green box and there are as many pens in the red box as there are in the pink box. How many pens are there in the green box?
We are given that Blue + Yellow = Pink pens
Pink = $$\frac{3}{2}\times\ $$ Yellow pens
Black = $$2\times\ $$Yellow pens
Red = $$2\times\ $$ Green pens
Red = Pink pens
From this, we can get, Red=Pink = $$2\times\ $$Green= $$\frac{3}{2}\times\ $$ Yellow
Giving, $$\frac{Green}{Yellow}=\frac{3}{4}$$, where we can take Green pens to be 3x and Yellow pens to be 4x(x is a constant).
From this, we can find the remaining pens in terms of x.
Green: 3x
Yellow: 4x
Red: 6x
Pink: 6x
Blue: 2x (Blue + Yellow = Pink)
Black: 8x
On adding all of them up we get 29x pens, we know that the total number of pens are 290, giving us the value of x to be 10.
Therefore the number of green pens in the box are $$3\times\ 10$$ = 30
