Inequality

Question

a party planner is reserving rooms for a corporate event and has at most 1000 dolars to spend. Sunrise room costs 180 dolars per hour. With a service charge of 100 dolars. At most, how many hours can the party planner rent the room for?

Answer 1

So, you know your cap is $1000, of which  $100 is deducted as a service fee and you still need to use an hourly rate of $180. We can express this algebraically as: 

 

1000 = 100 + 180x where x = the number of hours the question is asking for. 

 

We can rearrange this for like terms:

 

1000 - 100 = 900 = 180x => x = 5 hours.

 

That is the maximum number of hours that can be used.

Answer 2

180h + 100 ≤ 1000

180h ≤ 900 

h ≤ 900/180

h ≤ 5 hours