One month Donna rented 5 movies and 6 video games for a total of $48. The next month she rented 3 movies and 2 video games for a total of $18. Find the
rental cost for each movie and each video game.
Rental cost for each movie: s]
x
5
?
Rental cost for each video game: S

Cost for each movie: $1.50 Cost for each video game: $6.75

Step-by-step explanation:

Let x be the cost (in dollars) of renting a movie.

Let y be the cost (in dollars) of renting a video game.

The total cost of renting 3 movies and 2 video games is +3x2y dollars.

We're given that this total cost is $18, so we have =+3x2y18.

The total cost of renting 5 movies and 6 video games is +5x6y dollars.

We're given that this total cost is $48, so we have =+5x6y48.

Therefore, we get the following system of equations.

=+3x2y18

=+5x6y48

Multiplying the first equation by −3 and adding gives us the following.

   −9 x− 6 y = −54      5 x+ 6 y =  48     −4 x+ 0 y = −6  

So we get the equation =−4x−6.

Solving for x, we get the following.

=x1.5

To find y, we can substitute 1.5 for x in =+3x2y18, the first equation in the system.

Then we solve for y.

+31.52y=18

+4.52y=18

2y=13.5

y=6.75

So, we have found that =x1.5 and =y6.75.

This means that the rental cost for each movie is $1.50 and the rental cost for each video game is $6.75.

so, converting firstly the mixed fractions to improper fractions and then "adding".