Find number of spades in the set?

Question

 Dilip pics 19 cards from a pack of well shuffled card of which 10 are red and 9 are black.if there are twice as many heart as club and thrice as many diamond as club. 

Answer 1

(black) spades: a

hearts: 2b

diamonds: 3b

(black) clubs: b

 

5b = 10 so b=2

a+b = 9 so a=7; there are seven spades in the selected set of 19.

Answer 2

H = 2C

D = 3C

 

H+d+c+s = 2c+3c +c + s = 6c + s=19

 

s+c=9 <--- 9 black cards

 

s = 9-c

 

6c + 9-c = 19

5c + 9 = 19

5c = 10

c=2

 

 

 

2 clubs

7 spades

4 hearts

6 diamonds