The weekly rentals for a newly released DVD of an animated film at a local video store decreased each week.At the same time, the weekly rentals for a newly released DVD of a horror film increased each week.Models that approximate the weekly rentals R for each DVD are
$$\left\{ \begin{array} { l l }
R = 380 - 24 x & \text { Animated film } \
R = 28 + 20 x & \text { Horror film }
\end{array} \right.$$ where x represents the number of weeks each DVD was in the store, with x = 1 corresponding to the first week.After how many weeks will the rentals for the two movies be equal

A)10 weeks
B)6 weeks
C)4 weeks
D)12 weeks
E)8 weeks

Question

The weekly rentals for a newly released DVD of an animated film at a local video store decreased each week.At the same time, the weekly rentals for a newly released DVD of a horror film increased each week.Models that approximate the weekly rentals R for each DVD are
 $$\left\{ \begin{array} { l l } 
R = 380 - 24 x & \text { Animated film } \
R = 28 + 20 x & \text { Horror film }
\end{array} \right.$$   where x represents the number of weeks each DVD was in the store, with x = 1 corresponding to the first week.After how many weeks will the rentals for the two movies be equal 
 
A)10 weeks
B)6 weeks
C)4 weeks
D)12 weeks
E)8 weeks

Quizplus · Accepted Answer

To find when the rentals for the two movies will be equal, set the two equations equal to each other and solve for $x$:$$380 - 24x = 28 + 20x$$Combining like terms:$$352 = 44x$$Solving for $x$:$$x = 8$$Therefore, after 8 weeks, the rentals for the two movies will be equal.

The Weekly Rentals for a Newly Released DVD of an Animated