Question

Caitlin has a movie rental card worth $175. After she rents the first movie, the card’s value is
$172.25. After she rents the second movie, its value is $169.50. After she rents the third movie,
the card is worth $166.75.
Assuming the pattern continues, write an equation to define A(n), the amount of money on the
rental card after n rentals.
Caitlin rents a movie every Friday night. How many weeks in a row can she afford to rent a movie,
using her rental card only? Explain how you arrived at your answer.

Answer 1

The equation A(n)= $175 –(n x $2.75) would define the amount of money on the
rental card after (n) rentals.

According to the pattern given, $2.75 will be deducted to the rental card every after Caitlin rents a movie. We can simply divide the amount of the card which is $175 by $2.75 which we presume the rental fee. From that, we can have a result of 63.63 rentals using her card. Therefore, there will be 63.63 weeks Caitlin can afford to rent a movie.