During a promotional period, an online movie service charged a flat subscription fee of $12 for the month plus $7 for each movie rented. If Nadine’s total charge for the month was $89, how many movies did she rent that month?
For flat-fee plus per-item cost problems, quickly define a variable for the unknown quantity, write an equation in the form flat fee + (rate)·(quantity) = total, and solve step by step (subtract the flat fee, then divide by the rate). If you’re unsure, you can also plug each answer choice into the cost expression to see which one gives the stated total, but setting up and solving the equation is usually faster and less error-prone.
Hints
Write an expression for the total cost
Let a variable represent the number of movies rented. How would you write an expression that combines the $12 flat fee and $7 for each movie?
Set up the equation
Once you have an expression for the total cost, set it equal to $89, the amount Nadine was charged. What equation do you get?
Solve step by step
After you have your equation, first subtract the flat fee from both sides, then divide by the cost per movie to find the number of movies.
Desmos Guide
Enter the cost equation as a graph
In Desmos, type y = 12 + 7x to represent the total cost for renting movies.
Enter the total charge as a horizontal line
On the next line, type y = 89 to represent Nadine’s actual total charge.
Find the intersection point
Look for the point where the two graphs intersect and tap it. The x-coordinate of this intersection is the number of movies that makes the total cost $89.
Step-by-step Explanation
Translate the situation into an equation
Let be the number of movies Nadine rented.
She pays a flat subscription fee of $12 plus $7 for each movie, so her total cost can be written as
This equation says: starting from $12, add $7 for each of the movies, and the total is $89.
Isolate the term with the variable
To solve for , first get the term with by itself.
Subtract from both sides of the equation:
which simplifies to
Solve for the number of movies and check
Now divide both sides of by to solve for :
So Nadine rented movies. Check: , which matches the total charge. Therefore, the correct answer is 11 (choice C).