Question

Duke pays $111.60 for his yearly movie pass plus $4.00 for popcorn for each movie.Tenneshia pays $16.40 for a ticket to every movie but she doesn't buy food because she doesn't want to waste the money. In how many movies will they have paid the same amount?

Answer 1

After 9 movies they will have paid the same amount

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

`C = 111.60 + 4.00x`

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

`C = 16.40x`

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

`111.60 +4.00x=16.40x\\\\16.40x - 4x = 111.60\\\\12.40x =111.60\\\\x =(111.60)/(12.40)\\\\x =9`

After 9 movies they will have paid the same amount