x = Neil

200-x = Lucy.



    x - 50 = 3*(200-x)

    x - 50 = 600 - 3x

    x + 3x = 600 + 50

    4x     = 650

     x     = 650/4 = 162.50.


ANSWER.  Neil had initially $162.50.

    The question in the post is posed very sloppy.

You will look for two equations in two unknowns.



The first equation is Neil (N) plus Lucy's (L) total amount:

N + L = 200    (1)



The 2nd equation comes from the info about Neil spending $50 then having 3 times Lucy's amount:

N - 50 = 3L    (2)



These can be solved for L and N.  For example, I solved (2) for N (N = 3L+50) and then substituted the RHS for N in (1) which gave me   L=$37.50,  then using this value of L in (1) I computed N=$162.50



I've checked these values meet the two conditions, and you should too.



 

Answer by greenestamps(13215)   (Show Source): You can put this solution on YOUR website!
 


Let x be the amount Lucy had.


Then the amount Neil had (at the beginning) was 3x+50.  (After spending $50, he had 3 times as much as Lucy.)


Together in the beginning they had $200:









The amount Neil had at the beginning was 3x+50 = $112.50+$50 = $162.50.


(or, the amount he had at the beginning was $200-$37.50 = $162.50)


 

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