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Gavin has a points card for a movie theater.

He receives 20 rewards points just for signing up.
He earns 9.5 points for each visit to the movie theater.
He needs 77 points for a free movie ticket.

Which equation could be used to determine vv, the number of visits Gavin must make to earn a free movie ticket?

1 answer

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.

  1. He receives 20 points just for signing up.
  2. He earns 9.5 points for each visit. Therefore, for \( v \) visits, he would earn \( 9.5v \) points.
  3. 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.