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:
[tex]\begin{gathered} 3m+5v=39 \\ 9m+7v=63 \end{gathered}[/tex]We solve for m in 3m+5v=39:
[tex]\begin{gathered} 3m+5v=39 \\ Simplify\text{ and rearrange} \\ 3m=39-5v \\ m=\frac{39-5v}{3} \end{gathered}[/tex]Next, we plug in the value of m into 9m+7v=63:
[tex]\begin{gathered} 9m+7v=63 \\ 9(\frac{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=\frac{54}{8} \\ v=6.75 \end{gathered}[/tex]Then, we plug in v=6.75 into m=(39-5v)/3:
[tex]\begin{gathered} m=\frac{39-5v}{3} \\ m=\frac{39-5(6.75)}{3} \\ Simplify \\ m=1.75 \end{gathered}[/tex]Therefore,
Rental cost for each movie = $1.75
Rental cost for each video game= $6.75
