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
2 dramas, 6 comedies and 3 documentaries
1 dramas, 4 comedies and 6 documentaries
4 dramas, 3 comedies and 4 documentaries

Answer 1

Solve the following simultaneous equation for dram, com and doc. The first, second and third equations reflect Gina, Sam and Robbies rentals respectively. \[\{ 11= \text{dram} +\text{com}+\text{doc},27=2 \text{dram}+3 \text{com}+2\text{doc},19=\text{dram}+2\text{com}+2\text{doc}\} \]The answer for Gina is:\[\{\text{dram}\to 3,\text{com}\to 5,\text{doc}\to 3\} \]and is not one of the three solutions offered in the problem statement.