Let the No. of Cards with Raphael = x
the No. of Cards with James = y,
According to Question, x + y = 480 ----- (1)
Now No. of Cards given by Raphael to James = x/4
Cards with Raphael = 3x/4 ------- (2)
and No. of Present cards with James = [y + 3x/4] --- (3)
Now James given 1/3 of his total cards,
1/3[y + x/4] = y/3 + x/12 = (4y + x)/12 ----- (4)
New position of Cards left with James
= [y + x/4] - [(4y + x)/12]
= y + x/4 - 4y/12 - x/12
= (12y + 3x - 4y - x)/12 = (2x + 8y)/12 ------ (5)
and Raphael will left with
3x/4 + [(4y + x)/12] = 3x/4 + (4y+x)/12 = (9x + 4y + x)/12
= (10x + 4y)/12 ----- (6)
equating (5) and (6)
2x + 8y = 10x + 4y
or 8x = 4y => y = 2x ------ (7)
put this value y in (1)
x + 2x = 480
3x = 480
x = 160 cards
y = 320 cards
James had 320 cards in the beginning