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?
Answer

3 dramas, 5 comedies and 3 documentaries

1 dramas, 4 comedies and 6 documentaries

2 dramas, 6 comedies and 3 documentaries

Answer 1

set up:

gina = a + b + c = 11
sam = 2a + 3b + 2c = 27
Robby = a + 2b + 2c = 19

solve the system of linear equations for a b and c:

a = 3
b = 5
c = 3

I used augmented coefficient matrices to find a b and c, if you don't know that use the subtraction method for solving systems of linear equations

Answer 2

if you are given those answers ahead of time like multiple choice you an try plugging in the possible answers into the equations i made until you find one that works for all 3 people