Let's set x for each movie
Set y for each video.
Now, we have the next given information:
One month Latoya rented 2 movies and 3 video games.
We can write the next equation:
2x + 3y = 19
Also, the next she rented 4 movies and 8 video games.
We can write the next equation:
4x + 8y = 49
With both equations with the same variables, we have a system of equations:
1) 2x + 3y = 19
2) 4x + 8y = 49
Solve the system of equations using the elimination method.
First, multiply the first function by 4 and then multiply the second function by 2.
4(2x + 3y = 19)
8x +12y =76
and
2(4x + 8y = 49)
8x + 16y = 98
Subtract both functions:
[tex]\begin{gathered} 8x+12y=76 \\ 8x+16y=98 \\ --------------- \\ (8x-8x)+(12y-16y)=(76-98) \\ 0-4y=-22 \\ \text{Solve for y:} \\ y=\frac{-22}{-4} \\ y=5.5 \end{gathered}[/tex]
With the y value, we can replace it on the first function:
[tex]\begin{gathered} 2x+3y=19 \\ 2x+3(5.5)=19 \\ \text{Solve for x:} \\ 2x+16.5=19 \\ 2x=2.5 \\ x=\frac{2.5}{2} \\ x=1.25 \end{gathered}[/tex]
Hence:
The rental cost for each movie is $1.25
The rental cost for each video game is $5.5
