Question 68·Medium·Linear Equations in One Variable
Luis buys a movie club card for $15 and then pays $7 for each movie ticket he purchases. If his total spend is $64, how many movie tickets does Luis buy?
For linear word problems about total cost, quickly define a variable for the unknown quantity, then translate the situation into an equation of the form (fixed cost) + (rate × quantity) = (total). Carefully match each number in the problem to its role—fixed fee, per-item cost, or total—and then solve the one-variable equation by isolating the variable with inverse operations. If you have time, plug your answer back into the original cost expression to verify it gives the stated total.
Hints
Turn words into an equation
Identify the fixed cost and the cost that depends on the number of tickets. How can you write an expression for the total cost in terms of the number of tickets ?
Set the total equal to 64
Once you have an expression for the total cost, set it equal to 64, since that is how much Luis spends altogether.
Solve step by step
After writing the equation, first move the constant term (the fixed fee) to the other side. Then, how can you undo multiplying by 7 to get by itself?
Desmos Guide
Graph the cost and find the intersection
In Desmos, enter y = 15 + 7x to represent Luis’s total cost as a function of the number of tickets, and enter y = 64 to represent the total amount he spends. Then, look at the point where the two graphs intersect; the x-coordinate of that intersection is the number of movie tickets Luis buys.
Step-by-step Explanation
Define the variable
Let be the number of movie tickets Luis buys.
We want to find the value of that matches his total spending of .
Write an equation from the situation
Luis pays a fixed $15 for the movie club card, plus $7 for each ticket.
So his total cost is
We are told this total equals $64, so the equation is
Isolate the term with the variable
To start solving for , subtract from both sides to move the fixed fee to the other side:
Solve for the number of tickets
Now divide both sides of by to get alone:
So Luis buys movie tickets, which corresponds to choice C.