Question

Jose has a points card for a movie theater.
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.