Jose has a points card for a movie theater.

Question

He receives 50 rewards points just for signing up.
He earns 3.5 points for each visit to the movie theater.
He needs at least 85 points for a free movie ticket.

Write and solve an inequality which can be used to determine xx, the number of visits Jose can make to earn his first free movie ticket.

Answer 1

To determine the number of visits \( x \) that Jose can make to earn his first free movie ticket, we can set up an inequality based on the information provided.

1. Initial Points: Jose starts with 50 points.
2. Points Earned per Visit: He earns 3.5 points for each visit.
3. Total Points Needed: He needs at least 85 points for a free movie ticket.

We can express the total points Jose has after \( x \) visits as follows:

\[ \text{Total points} = 50 + 3.5x \]

We want this total to be at least 85 points, so we set up the inequality:

\[ 50 + 3.5x \geq 85 \]

Now, we will solve the inequality for \( x \):

1. Subtract 50 from both sides:

\[ 3.5x \geq 85 - 50 \]

\[ 3.5x \geq 35 \]

2. Divide both sides by 3.5:

\[ x \geq \frac{35}{3.5} \]

Calculating \( \frac{35}{3.5} \):

\[ \frac{35}{3.5} = 10 \]

So the solution to the inequality is:

\[ x \geq 10 \]

This means that Jose needs to make at least 10 visits to the movie theater to earn his first free movie ticket.