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 1<br />The 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.<br /><br />## Step 2<br />We can represent this situation with the equation:<br />### \(85 + 7.5v = 160\)<br /><br />## Step 3<br />To solve for v, we first subtract 85 from both sides of the equation:<br />### \(7.5v = 160 - 85\)<br /><br />## Step 4<br />This simplifies to:<br />### \(7.5v = 75\)<br /><br />## Step 5<br />Next, we divide both sides of the equation by 7.5 to solve for v:<br />### \(v = \frac{75}{7.5}\)