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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.

Verified Answer :

First, let's find out the amount it costs to rent one movie.

175-172.25=2.75
172.25-169.50=2.75
169.50-166.75=2.75

$2.75/movie rental
-----------------------------------------------------------
A=175-2.75n

where a is the amount on the card
175 is the original amount in the card
2.75 is the cost of a movie rental times n amount of rentals
-------------------------------------------------------------------------------
n=175/2.75
  =63.63
  =63

n is the amount of weeks she can rent a movie  

She can rent movies for 63 weeks in a row

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