Ryan has a points card for a movie theater.

Question

He receives 85 rewards points just for signing up.
He earns 7.5 points for each visit to the movie theater.
He needs 160 points for a free movie ticket.

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

Answer 1

To determine the number of visits \( v \) Ryan must make to earn a free movie ticket, we can start by writing an equation based on the information provided.

1. Ryan starts with 85 points from signing up.
2. He earns 7.5 points for each visit he makes to the movie theater.
3. He needs a total of 160 points to receive a free movie ticket.

The total points Ryan has after \( v \) visits can be expressed as:

\[ 85 + 7.5v \]

We need to set this equal to the number of points required for a free movie ticket, which is 160 points:

\[ 85 + 7.5v = 160 \]

Now, we can solve for \( v \):

1. Subtract 85 from both sides of the equation:

\[ 7.5v = 160 - 85 \]

\[ 7.5v = 75 \]

2. Now, divide both sides by 7.5 to find \( v \):

\[ v = \frac{75}{7.5} \]

\[ v = 10 \]

Therefore, Ryan must make 10 visits to earn a free movie ticket.