Question

Adam has a points card for a movie theater.He receives 60 rewards points just for signing up.He earns 12.5 points for each visit to the movie theater.He needs at least 160 points for a free movie ticket.Use the drop-down menu below to write an inequality representing v, the number of visits he needs to make in order to get a free movie ticket.

Answer 1

We have to write an inequality that represents this situation.

Since he received 60 points for signing up, 60 will be a constant that makes part of the inequality.

He earns 12.5 points for each visit, let v be the number of visits, then he will earn 12.5v points after v visits.

The sum of 12.5v and 60 is the total amount of points he will have, and this has to be at least 160 to get a free movie ticket, it means that 12.5v+60 is greater than or equal to 160:

`12.5v+60\ge160`

Solve the inequality to find the number of visits he needs to make to get a free movie ticket:

`\begin{gathered} 12.5v+60\ge160 \\ 12.5v+60-60\ge160-60 \\ 12.5v\ge100 \\ v\ge(100)/(12.5) \\ v\ge8 \end{gathered}`

It means that he needs to make at least 8 tickets to get a free movie ticket.