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There were some red, black and blue pens in a drawer. 1/3 of the pens were red and the number of black pens was 11 less than 1/2 of the number of red pens. If there were 284 blue pens, how many black pens were there in the drawer?

 Aug 11, 2021
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given data in

1/3rd of the pens are red.

number of black pens was 11 pens then 1/2 of the red pens.

There were total 284              blue pens.

To find number of black pens.

 

Assume that there are x red pen, y black pens, z blue pens, then

 

 

                      x = 1/3 (x + y + z)

                      z = 284    and         y+11=1/2x

=>        3x = x + y + z   ;  z = 284  ;   2y+22=x

            2x-y=284            x-2y=22

 

 

            2(2y+22)-y=284

               4y + 44 - y = 284

                 3y = 240

                   y = 80       x = 2 (80) + 22 = q82

                                    x = 182

Thus there were total 80 black pens.

 Aug 11, 2021

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