Question

One month Milan rented 6 movies and 5 video games for a total of $50. The next month he rented 2 movies and 3 video games for a total of $24. Find the rental cost for each movie and each video game.

Answer 1

Given :

The cost of rent 6 movies and 5 video games is 50 dollar.

The cost of rent 2 movies and 3 video games is 24 dollar.

Explanation :

Let the rental cost of movies be denoted as M.

Let the rental cost of video games be denoted as V.

Then the equation formed from the given data is

`\begin{gathered} 6M+5V=50\ldots\ldots\ldots\ldots\ldots\ldots\ldots1 \\ 2M+3V=24\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots2 \end{gathered}`

Solve the following equations by elimination method ,

Multiply by 3 in equation 2.

`6M+9V=72\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots..3`

Now solve the equation 1 and 3 and find value of M and V.

`\begin{gathered} (6M+5V-50)-(6M+9V-72)=0 \\ 5V-9V-50+72=0 \\ -4V=-22 \\ V=5.5 \end{gathered}`

Now substitute the value of V in the equation 1 to find M.

`\begin{gathered} 6M+5*5.5=50 \\ 6M=50-27.5 \\ M=(22.5)/(6) \\ M=3.75 \end{gathered}`

Answer:

Hence the rental cost of each movie is 3.75 dollar and rental cost of each video games is 5.5 dollar.