Layla has a points card for a movie theater.

Question

She receives 60 rewards points just for signing up.
She earns 11.5 points for each visit to the movie theater.
She needs 129 points for a free movie ticket.

Write and solve an equation which can be used to determine xx, the number of visits Layla must make to earn a free movie ticket.

Answer 1

To determine the number of visits \( x \) that Layla must make to earn a free movie ticket, we can set up an equation based on the points she earns.

Layla starts with 60 points from signing up and earns 11.5 points for each visit. Therefore, the total points she will have after \( x \) visits can be represented by the expression:

\[ 60 + 11.5x \]

Since she needs 129 points for a free movie ticket, we can set up the equation:

\[ 60 + 11.5x = 129 \]

Now, let's solve for \( x \):

1. Start by isolating the term with \( x \):

\[ 11.5x = 129 - 60 \]

2. Simplify the right side:

\[ 11.5x = 69 \]

3. Now, solve for \( x \) by dividing both sides by 11.5:

\[ x = \frac{69}{11.5} \]

4. Calculate \( x \):

\[ x = 6 \]

Thus, Layla must make 6 visits to the movie theater to earn enough points for a free movie ticket.