Respuesta :
Let "m" represent the cost of one movie rent and "v" represent the cost of one videogame rent.
One month she rented 3 movies and 2 videogames for a total of $21, you can express the total cost for this month as:
[tex]3m+2v=21[/tex]Another month she rented 8 movies and 4 video games for a total of $49, you can express the rental costs for this month as follows:
[tex]8m+4v=49[/tex]These expressions form an equation system. To solve it, the first step is to write one of the equations in terms of one of the variables, for example, write the first equation for "v"
[tex]\begin{gathered} 3m+2v=21 \\ 3m-3m+2v=21-3m \\ 2v=21-3m \\ \frac{2v}{2}=\frac{21}{2}-\frac{3}{2}m \\ v=\frac{21}{2}-\frac{3}{2}m \end{gathered}[/tex]Next, replace the expression obtained for "v" into the second equation and solve for "m"
[tex]\begin{gathered} 8m+4v=49 \\ 8m+4(\frac{21}{2}-\frac{3}{2}m)=49 \end{gathered}[/tex]-Distribute the multiplication on the parentheses term:
[tex]\begin{gathered} 8m+4\cdot\frac{21}{2}-4\cdot\frac{3}{2}m=49 \\ 8m+42-6m=49 \end{gathered}[/tex]-Order the like terms together and simplify them:
[tex]\begin{gathered} 8m-6m+42=49 \\ 2m+42=49 \end{gathered}[/tex]-Pass 42 to the right side of the equation by applying the opposite operation to both sides of the equal sign:
[tex]\begin{gathered} 2m+42-42=49-42 \\ 2m=7 \end{gathered}[/tex]-Divide both sides by 2 to determine the value of m:
[tex]\begin{gathered} \frac{2m}{2}=\frac{7}{2} \\ m=\frac{7}{2}\approx3.5 \end{gathered}[/tex]-Replace the value obtained for "m" on the expression for "v" to determine the rental cost of one video game:
[tex]\begin{gathered} v=\frac{21}{2}-\frac{3}{2}m \\ v=\frac{21}{2}-\frac{3}{2}\cdot\frac{7}{2} \\ v=\frac{21}{2}-\frac{21}{4} \\ v=\frac{21}{4}\approx5.25 \end{gathered}[/tex]The rental cost for the movies is m=$3.50/movie and the rental cost for the videogames is v=$5.25/video game
