Question

One month Lucy rented 3 movies and 5 video games for a total of $39. The next month she rented 9 movies and 7 video games for a total of $63. Find the rental cost for each movie and each video game.Rental cost for each movie:Rental cost for each video game:Solve by using system of linear equations.

Answer 1

Given the word problem, we can deduce the following information:

1. One month Lucy rented 3 movies and 5 video games for a total of $39.

2. The next month she rented 9 movies and 7 video games for a total of $63.

To determine the rental cost for each movie and each video game, we first let:

m= Rental cost for each movie

v= Rental cost for each video game

Hence, the linear equations would be:

`\begin{gathered} 3m+5v=39 \\ 9m+7v=63 \end{gathered}`

We solve for m in 3m+5v=39:

`\begin{gathered} 3m+5v=39 \\ Simplify\text{ and rearrange} \\ 3m=39-5v \\ m=(39-5v)/(3) \end{gathered}`

Next, we plug in the value of m into 9m+7v=63:

`\begin{gathered} 9m+7v=63 \\ 9((39-5v)/(3))+7v=63 \\ Simplify\text{ and rearrange} \\ 3(39-5v)+7v=63 \\ 117-15v+7v=63 \\ 117-8v=63 \\ 8v=117-63 \\ 8v=54 \\ v=(54)/(8) \\ v=6.75 \end{gathered}`

Then, we plug in v=6.75 into m=(39-5v)/3:

`\begin{gathered} m=(39-5v)/(3) \\ m=(39-5(6.75))/(3) \\ Simplify \\ m=1.75 \end{gathered}`

Therefore,

Rental cost for each movie = $1.75

Rental cost for each video game= $6.75