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 , the number of visits Ryan must
make to earn a free movie ticket.

Question

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 , the number of visits Ryan must
make to earn a free movie ticket.

UpStudy AI · Accepted Answer

To determine the number of visits $$ v $$ that Ryan must make to earn a free movie ticket, we can set up an equation based on the points he earns.

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

The total points Ryan has after $$ v $$ visits can be expressed as:

$$
\text{Total Points} = 85 + 7.5v
$$

To find out how many visits he needs to make to reach 160 points, we set up the equation:

$$
85 + 7.5v = 160
$$

Now, we can solve for $$ v $$:

1. Subtract 85 from both sides:

$$
7.5v = 160 - 85
$$

$$
7.5v = 75
$$

2. Divide both sides by 7.5:

$$
v = \frac{75}{7.5}
$$

$$
v = 10
$$

Thus, Ryan must make $$ \boxed{10} $$ visits to earn a free movie ticket.
Ryan must make 10 visits to earn a free movie ticket.

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