Math Question!!!?

Question

Danish and George each have some Pokemon cards. If Danish gives 24 cards to George, both of them will have the same number of cards. If George gives 15 cards to Danish, the number of cards that Danish has to the number of cards George has will be in the ratio 7:1. How many Pokemon cards does each boy have?

Answer 1

let, danish's cards be x
george's cards be y

x - 24 = y + 24
x - y = 48................A

(x + 15)/(y - 15) = 7
x + 15 = 7y - 105
x - 7y = -120............B

subract A and B, you'll get,

6y = 168
y = 28

x = 48 + y
x = 76

Danish has 76 cards.
George has 28 cards.

Answer 2

Let George have g cards

Danish has g+48 cards because if he gives 24 to George then they both have g+24 cards.

If George gives 15 cards to Danish then he now has g-15 and Danish has g+48+15 (ie g+63)

(g+63) / (g-15) = 7/1 according to the ratio

g+63 = 7g - 105
105 + 63 = 6g
g = 168 / 6

George has g = 28 cards
Danish has 76 cards

Answer 3

Take 2 variables D and G for Danish's and George's cards. In the first case:
D - 24 = G + 24
D = G + 48

In the second case:
(G - 15) / (D + 15) = 1 / 7

7G - 105 = D + 15
7G = D + 120
7G = G + 48 + 120 (from the first case)
6G = 168

G = 28
D = 76

George has 28 cards and Danish has 76 cards.

Answer 4

impossible! George must have a negative amount of cards