Question

You like to watch movies at the local cinema. You have two payment options. Option a is to buy a discount card which will cost you $160, and then $20 per movie. Option b is to pay $40 per movie. After how many movies will the total costs of the two options be the same? Write a system of equations in order to solve the problem.

Answer 1

Let us consider the case : a discount card which will cost you $160, and then $20 per movie.

For x number of movies, Your cost is,

$160+20x$

Taking the second case: $40 per movie. Foe x number of movies, your cost is,

$40x$

So, when the total cost is same,

$\begin{gathered} 160+20x=40x \\ 160=40x-20x=20x \\ \frac{160}{20}=x \\ x=8 \end{gathered}$

So after 8 movies, the total costs of the two options will be the same.