Question

One month Jenny rented 2 movies and 3 video games for a total of $19. The next month she rented 4 movies and 8 video games for a total of $49. Find the rental cost for each movie and each video game.

Answer 1

Let be "m" the rental cost for each movie (in dollars) and "v" the rental cost for each video game (in dollars).

Based on the explanation given in the exercise, you can set up the following System of equations:

`\begin{cases}2m+3v=19 \\ 4m+8v=49\end{cases}`

You can solve it using the Elimination method:

1. Multiply the first equation by -2.

2. Add the equations.

3. Solve for "v":

`\begin{gathered} \begin{cases}-4m-6v=-38 \\ 4m+8v=49\end{cases} \\ ------------ \\ 2v=11 \\ \\ v=(11)/(2) \\ \\ v=5.5 \end{gathered}`

4. Substitute the value of "v" into any original equation:

`\begin{gathered} 2m+3v=19 \\ 2m+3(5.5)=19 \\ 2m=19-16.5 \\ \\ m=(2.5)/(2) \\ \\ m=1.25 \end{gathered}`

The answer is:

- Cost for each movie: $1.25

- Cost for each video game: $5.5