19. A group of pirates (raiders, sailors and cabin boys) divided 200 gold and 600 silver coins between them. Each raider received 5 gold and 10 silver coins. Each sailor received 3 gold and 8 silver coins. Each cabin boy received 1 gold and 6 silver coins. How many pirates were there altogether?
A 50
B 60
C 72
D 80
E 90
SOLUTION
D

Let $R$ be the number of raiders, $S$ the number of sailors and $C$ the number of cabin boys. Then the number of gold coins is $5 R+3 S+C=200$ [1]. The number of silver coins is $10 R+8 S+6 C=600$ [2]. Subtracting [1] from [2] gives $5 R+5 S+5 C=400$, so $R+S+C=80$.