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 1

Let x = the number of dramas Gina rented, y the number of comedies Gina rented and z the number of documentaries.

Answer 2

x+y+z=11

Answer 3

2x+3y+2z =27

Answer 4

x+2y+2z=19

Answer 5

But what types of movies did she buy in what quantities?

Answer 6

To work that out we will need to solve the above equations..

Answer 7

ok

Answer 8

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

Answer 9

2x + 2y + 2z = 22
–x –2y – 2z = –19
Add these two equations.. What will x be?

Answer 10

x+0+0=3 or x=3

Answer 11

Now we multiply equation 1 by -2 and then add equation 2

Answer 12

This gives us:
–2x – 2y – 2z = –22
2x + 3y + 2z = 27

Now we add these together and get y=5

Answer 13

Now plug x=3 and y=5 into equation 1 and you get 3+5+z=11
Therefore z=3

Answer 14

Therefore Gina rented 3 dramas 5 comedies and 3 documentaries.. This question was a hard one just due to the sheer quantity of data supplied, however they can be done just by working each set of facts into equations and solving from there.