To determine the number of visits \( v \) that Gavin must make to earn a free movie ticket, we can start with his initial points and the points he earns per visit.
- He receives 20 points just for signing up.
- He earns 9.5 points for each visit. Therefore, for \( v \) visits, he would earn \( 9.5v \) points.
- He needs a total of 77 points to redeem a free ticket.
We can set up the equation by adding his initial points to the points earned from his visits and setting that equal to the points needed for a free ticket:
\[ 20 + 9.5v = 77 \]
This is the equation that can be used to determine \( v \), the number of visits Gavin needs to make.
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