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

We need to find the value of x at which R(anime) = R(horror).

Setting the two models equal to each other we get:

50 - 7x = 3x + 2

Simplifying and solving for x we get:

10x = 48

x = 4.8

Since x represents weeks, we need to round up to the closest integer, which is 5.

Therefore, after 5 weeks, the weekly rentals for the two movies will be equal.

The closest answer choice is E (8 weeks), but this is not the correct answer.

The Weekly Rentals for a Newly Released DVD of an Animated