Question

1. leah has a points card for a movie theater.

• she receives 75 rewards points just for signing up.
• she earns 14.5 points for each visit to the movie theater.
• she needs 162 points for a free movie ticket.

write and solve an equation which can be used to determine $x$, the number of visits leah must make to earn a free movie ticket.

Explanation:

Step1: Define total points equation

Total points = sign-up points + points per visit × number of visits.
$$75 + 14.5x = 162$$

Step2: Isolate the variable term

Subtract 75 from both sides.
$$14.5x = 162 - 75$$
$$14.5x = 87$$

Step3: Solve for x

Divide both sides by 14.5.
$$x = \frac{87}{14.5}$$
$$x = 6$$

Answer:

The equation is $75 + 14.5x = 162$, and Leah must make 6 visits.