Question

Gina, Sam and Robby all rented movies from the same video store. They each rented some dramas, comedies and documentaries. Gina rented 11 movies total. Sam rented twice as many dramas, three times as many comedies, and twice as many documentaries as Gina. He rented 27 movies total. If Robby rented 19 movies total with the same number of dramas, twice as many comedies, and twice as many documentaries as Gina, how many movies of each type did Gina rent?

A) 3 dramas, 5 comedies and 3 documentaries
B) 2 dramas, 6 comedies and 3 documentaries
C) 1 dramas, 4 comedies and 6 documentaries

Answer 1

x = number of dramas Gina rented
y = number of comedies Gina rented
z = number of documentaries Gina rented

Gina rented 11 movies total:
(1) x + y + z = 11

Sam rented twice as many dramas, 3 times as many comedies, and twice as many documentaries as Gina. He rented 27 movies total
(2) 2x + 3y + 2z = 27

Robby rented 19 movies total, with same number of dramas, twice as many comedies, and twice as many documentaries as Gina
(3) x + 2y + 2z = 19


Multiply equation 1 by 2 and multiply equation 3 by -1
2x + 2y + 2z = 22
–x –2y – 2z = –19

Add equations: x = 3


Multiply equation 1 by –2, then add equation 2
–2x – 2y – 2z = –22
2x + 3y + 2z = 27

Add equations: y = 5


Now plug x = 3 and y = 5 into equation 1
x + y + z = 11
3 + 5 + z = 11
8 + z = 11
z = 3


Solution: Gina rented
3 dramas
5 comedies
3 documentaries