If Will gives Molly $9, he will have the same amount of money as her. If Molly gives Will $9, the ratio of the money she has to the money Will has will be 1 : 2. How much money does Will have in the beginning?

Answer 1

Molly's original amount ---- x
Will's original amount ------y

after give-away:
Molly has x+9
Will has y-9
but then x+9 = y-9
y = x+18

after hypothetical other case:
Molly has x-9
Will has y+9

(x-9)/(x+9) = 1/2
2x - 18 = y+9
y = 2x - 27

so 2x - 27 = x + 18

x = 45 , then y = 63

check:
after 1st giveaway:
Molly has x+9 = 45+9 = 54
Will has y - 9 = 63-9 =54 , they have the same

after 2nd giveaway:
Molly has x-9 = 45-9 = 36
Will has y + 9 = 63+9 = 72 , which is twice the 36