Question

One month Brian rented 7 movies and 9 video games for a total of $78. The next month he rented 5 movies and 3 video games for a total of $36. Find therental cost for each movie and each video game.Rental cost for each movie.Rental cost for each video game:

Answer 1

The given question would form a simultaneous equation.

Let the cost of a movie be "x" and the cost of a video game by "y."

Therefore, when Brian rented 7 movies and 9 video games for a total of $78, this would form this equation.

`7x+9y=78-------\mleft\lbrace1\mright\rbrace`

When Brian rented 5 movies and 3 video games for a total of $36, this would give

`5x+3y=36--------\mleft\lbrace2\mright\rbrace`

To solve the simultaneous equation we need to create equation three and use the elimination method to eliminate one variable.

We would multiply equation two by 3 to get equation three

`\begin{gathered} 3(5x+3y=36) \\ 15x+9y=108-----\mleft\lbrace3\mright\rbrace \end{gathered}`

The next step would be to subtract equation two from equation three

`\begin{gathered} 15x-7y+9y-9y=108-78 \\ 8y=30 \\ y=(30)/(8) \\ y=3.75 \end{gathered}`

We would then substitute the value of "y" into equation two to get "x."