Ryan has a points card for a movie theater. - 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 v the number of visits Ryan must make to earn a free movie ticket.

## Step 1The problem involves the use of algebraic expressions to represent real-life situations. Ryan starts with 85 reward points and earns 7.5 points for each visit to the movie theater. We are asked to find out how many visits (v) Ryan needs to make to earn a free movie ticket, which is 160 points.## Step 2We can represent this situation with the equation:### ## Step 3To solve for v, we first subtract 85 from both sides of the equation:### ## Step 4This simplifies to:### ## Step 5Next, we divide both sides of the equation by 7.5 to solve for v:###