Help Please

x = number of marbles to add

the total number of marbles will be   20 + 40 + x    of which 40 will be green for a fraction of green:

40 / (20+40+x)  = 5/12      solve for x

40/(60+x) = 5/12

40 /  (5/12) = 60 + x

96    = 60 + x

x = 36 purple marbles need to be added

40 / (5/12) =96 total marbles needed

96 - (20+40) =36 new purple marbles needed.

Let x be the number of purple ones to be added.......and we have....

40 / [60 +  x]   = 5/12    cross multiply

40 [ 12]  = [60 + x] 5     simplify

480  = 300 + 5x         

180  =  5x

36   = x

Proof :

40 / [60+36]   =  40/ 96  = 5/12