A, b, c, and d play a game of cards. a says to b, "if i take away 6 cards from you, then you will have as many as c has and i shall have 3 more than what c has. also, if i take 5 cards from c, then i shall have twice as many as d". if b and d together have 25 cards, then how many cards does a have?

A has 9 cards

Given that, A says to B, "If I take away 6 cards from you, then you will have as many as C has. So, from the 1st relation between B and C we get.

B - 6 = C  

B = C + 6 eqn 1

And I shall have 3 more than what C has, Now, relationship between A and C can be given as:

A + 6 = C + 3

A + 6 - 3 = C

A + 3 = C   eqn 2

Also, if I take 5 cards from C, then I shall have twice as many as D", For the second condition, relation between A and D is:

A + 5 = 2D

A = 2D - 5   eqn 3

If B and D together have 25 cards, And, the relationship between B and D is given as:

B + D = 25   eqn 4

Now we have substitute eq1 in eq4 we get:

C + 6 + D = 25

Substitute eq2 in the above equation

A + 3 + 6 + D = 25

Now, we substitute the eq3 in the above equation to get:

2D - 5 + 3 + 6 + D = 25

3D + 4 = 25

3D = 21

D = 7

So, now we can substitute the value of D in eq3 to get the value of A as follows:

A = 2(7) - 5

A = 14 - 5

A = 9

Therefore, A has 9 cards.