Ryan has a points card for a movie theater.

Question

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

equation: _____

Answer x _____

Answer 1

To determine the number of visits Ryan must make to earn a free movie ticket, we can set up the following equation:

Let \( v \) be the number of visits Ryan makes.

Ryan starts with 85 points and earns 7.5 points for each visit. To find the total points Ryan has after \( v \) visits, we can express this as:

\[ 85 + 7.5v \]

Ryan needs 160 points for a free movie ticket, so we can set up the equation:

\[ 85 + 7.5v = 160 \]

Now, let's solve the equation for \( v \):

1. Subtract 85 from both sides: \[ 7.5v = 160 - 85 \] \[ 7.5v = 75 \]

2. Now, divide both sides by 7.5: \[ v = \frac{75}{7.5} \] \[ v = 10 \]

Thus, the equation and the solution are:

equation: \( 85 + 7.5v = 160 \)

Answer: \( v = 10 \)