Problem
Dante rented some movies and video games last month. He did the same this month. The table below shows the number of movies and video games he rented each month. It also shows the total cost (in dollars). \begin{tabular}{|c|c|c|} \hline & \begin{tabular}{c} Last \\ month \end{tabular} & \begin{tabular}{c} This \\ month \end{tabular} \\ \hline \begin{tabular}{c} Number of \\ movies \end{tabular} & 3 & 8 \\ \hline \begin{tabular}{c} Number of \\ video games \end{tabular} & 2 & 4 \\ \hline \begin{tabular}{c} Total cost \\ (in dollars) \end{tabular} & 18 & 41 \\ \hline \end{tabular} Let $x$ be the cost (in dollars) of renting a movie. Let $y$ be the cost (in dollars) of renting a video game. (a) Write a system of equations that could be used to find the rental cost (in doliars) for each movie and each video game. \[ \begin{array}{l} \square x+\square y=\square \\ \square x+\square y=\square \end{array} \] (b) How much did it cost (in dollars) to rent each movie and each video game? Rental cost for each movie: $\$$ आ Rental cost for each video game: $\$[$ Continue Save For Later Submit Assignment
Solution
Step 1 ：Let's denote the cost of renting a movie as x and the cost of renting a video game as y.
Step 2 ：From the table, we can see that last month Dante rented 3 movies and 2 video games for a total cost of $18. This gives us the equation \(3x + 2y = 18\).
Step 3 ：This month, he rented 8 movies and 4 video games for a total cost of $41. This gives us the equation \(8x + 4y = 41\).
Step 4 ：So, the system of equations is: \[\begin{array}{l}3x+2y=18 \\ 8x+4y=41\end{array}\]
Step 5 ：Solving this system of equations gives us the solution \(x = 2.5\) and \(y = 5.25\).
Step 6 ：So, the rental cost for each movie is \(\boxed{\$2.5}\) and the rental cost for each video game is \(\boxed{\$5.25}\).
