A network of hotels across the united states normally charges $\$150$ for an overnight stay at any of its properties. This network also offers a deal for longer trips. A traveller who purchases a hotel discount card of $\$750$ will pay only $\$120$ per night at any of network properties for the duration of the traveller's trip. Which of the following inequation represents the number of nights 'n' a traveller must stay in any combination of the networks hotel during a trip in order to make the discount card a better deal ?
