# 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 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:

$y = k x + c$

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 $\text{  "27" } m o v i e s = x\$