Question

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?

Answer 1

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.