Valley Video charges a $15 annual fee plus $3 per movie for rentals. Last year, Jennifer spent $99 at the store. How many movies did she rent?

1 Answer
Geoff K.
Dec 18, 2016

Jennifer rented 27 movies.

Explanation:

We seek a number of movies #x# such that the total cost for the year (#$99#) will equal the cost of the movie rentals (#$3x#) plus the cost for 1-year membership (#$15#).

This information models a linear relationship between the number of movies rented (#x#) and the amount spent in a year (#y#). For every 1 more movie, Jennifer pays 3 more dollars. This constant of "3 dollars per movie" can be considered the rate at which #y# responds to changes in #x#.

The equation that we use for a linear model is one like this:

#y=kx+c#

where, in this case,

  • #y# = total amount spent in a year,
  • #k# = cost per movie rental,
  • #x# = number of movie rentals, and
  • #c# = base fee for the year.

The given information lets us plug in values for three of these four variables, meaning we can solve for the fourth.

#color(white)(XXXX)$99=($3//movie) * x + $15#
#color(white)(XXXX)$84=($3//movie) * x#
#($84)/($3//movie)=x#

#"  "27" "movies = x#

And that's our answer.

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