Answer:
After 9 movies they will have paid the same amount
Step-by-step explanation:
We must write an equation for Duke's expenses and an equation to represent Tennessee's expenses.
For Duke expenses we have:
A fixed expense of $ 111.60 per year
A variable expense of $ 4.00 for each movie.
The equation that represents the expenses is a linear equation like the one shown below
[tex]C = 111.60 + 4.00x[/tex]
Where C represents the cost and x the number of movies.
For Tennessee expenses we have:
A variable expense of $ 16.40 for each film.
The equation that represents the expenses is a linear equation like the one shown below
[tex]C = 16.40x[/tex]
Where C represents the cost and x the number of movies.
To know after how many movies have paid the same amount, we equate both equations and solve the variable x
[tex]111.60 +4.00x=16.40x\\\\16.40x - 4x = 111.60\\\\12.40x =111.60\\\\x =\frac{111.60}{12.40}\\\\x =9[/tex]
After 9 movies they will have paid the same amount
