Question

Julian has a points card for a movie theater. He receives 85 rewards points just for signing up. He earns 3.5 points for each visit to the movie theater. He needs 120 points for a free movie ticket. Which equation or tape diagram could be used to represent the context if xx represents the number of visits Julian must make to earn a free movie ticket?

Answer 1

an equation that can be used to represent the number of visits needed to earn a free movie ticket is

3.5x+85=120

Explanation:

you would multiply 3.5 by the number of visits (x) to determine how many points Julian would have earned in total. you would add 85 to the product of 3.5(x) because he had started with 85 points.

if you want to find how many times Julian would need to visit the movie theater to get a free movie ticket you can subtract 85 from 120, to find out how many visits are necessary before adding the extra 85 points. subtracting that leaves you with 35, and if you divide that by 3.5, the number of points per visit, you are left with 10. Julian would need to visit the theater 10 times before earning a free movie ticket.

if you want to check to see if that's right, you can just do the equation in reverse. rather than 85-120=35/3.5=10, you can do 10*3.5=35+85=120

hope this helps