Respuesta :
A has 9 cards
Solution:
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.
