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# How to solve?

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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?

Aug 25, 2021

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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

Dec 27, 2021