+80 Raphael and James shared 480 game cards.
Raphael gave 1/4 of his cards to James.
James then gave 1/3 of the total number of cards he had to Ralphael.
In the end, they had the same number of cards.
How many cards did James have at first?
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
