A problem with playing cards?

Question

A deck of 52 playing cards is cut into 3 separate piles.

In the first pile there are 3 times as many blacks as reds.

In the second pile there are 3 times as many reds as blacks.

In the third pile there are twice as many blacks as reds.

How many cards of each colour are there in each of the three piles?

Answer 1

piles is a painfull thing to have!

Answer 2

wat the h**l is that??

8 black 10 red-1

10 black 8 red-2

8 black 8 red-3

this is probally wrong but watever...

Answer 3

12

Answer 4

Which pile has the spare card?

Answer 5

no solution

Answer 6

r1 + r2 + r3 = 26 = b1 + b2 + b3

b1 = 3r1

r2 = 3b2

b3 = 2r3

r1 + r2 + r3 = 3r1 + (r2)/3 + 2r3

2r1 + r3 = 2r2 /3

3r1 + 1.5r3 = r2 = b1 + 1.5r3

r2 > b1 --> b2 > r1

52 = 4r1 + 4b2 + 3r3 = 4(r1 + b2) + 3r3

so r3 is divisible by 4.

let r3 = 4x, then r1 + b2 = 13 - 3x > 0, 0 < x < 5

r2 = b1 + 6x < 26

b1 + b2 + b3 = (b1)/3 + 3b2 + (b3)/2

2(b1)/3 + (b3)/2 = 2b2

4b1 + 3b3 = 12b2

b1 = 12, b2 = 6, b3 = 8

r1 = 4, r2 = 18, r3 = 4

answers =

pile 1 : 16 = 12 blacks + 4 reds

pile 2 : 24 = 6 blacks + 18 reds

pile 3 : 12 = 8 blacks + 4 reds

sorry, incomplete working, but i think the answer works.