Question

One month lashonda rented 3 movies and 2 video games for a total of $19. The next month she rented 5 movies and 6 video games for a total of $47. Find the rental cost for each movie and each video game

Answer 1

We are given that:

Lashonda rented 3 movies and 2 video games for a total of $19. If "x" is the cost per movie and "y" the cost per video game, then we can write this mathematically as:

$3x+2y=19,(1)$

This is our first equation.

We are also given that:

She rented 5 movies and 6 video games for a total of $47. This can be written mathematically as:

$5x+6y=47,(2)$

This is our second equation.

To solve the system we will solve for "x" in equation (1). To do that we will subtract "2y" from both sides:

$3x=19-2y$

Now we divide both sides by 3:

$x=\frac{19-2y}{3}$

Now we substitute this in equation (1):

$5(\frac{19-2y}{3})+6y=47$

Now we use the distributive law on the parenthesis:

$\frac{95-10y}{3}+6y=47$

Now we multiply both sides by 3, we get:

$95-10y+18y=141$

Now we add like terms:

$95+8y=141$

Now, we subtract 95 from both sides:

$\begin{gathered} 8y=141-95 \\ 8y=46 \end{gathered}$

Dividing both sides by 8:

$y=\frac{46}{8}=5.75$

Now we substitute this value in equation (1), the one where we have solved for "x", we get:

$x=\frac{19-2(5.75)}{3}$

Solving the operations we get:

$x=2.5$

Therefore, each movie costs $2.5 and each video game costs $5.75.