October 8th, 2018, 01:15 PM  #1 
Senior Member Joined: Apr 2017 From: New York Posts: 119 Thanks: 6  inequality
Hi everyone. I am working on this question and the equations I set did not work. Any idea? Here is the word problem on inequality: High school X is looking into bringing their Physics students on a field trip to Bronx zoo. Tickets for the park normally cost \$65.5 per person. However, if they bring more than 55 students, the park will give \$2.5 discount per ticket for each student above 55 students. What is the minimum number of students that High school X needs to bring so that each student is not spending more than \$45 for their ticket? Last edited by skipjack; October 8th, 2018 at 03:17 PM. 
October 8th, 2018, 01:49 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,640 Thanks: 625 
Fix typos. As is there is no solution.

October 8th, 2018, 03:28 PM  #3 
Global Moderator Joined: Dec 2006 Posts: 19,950 Thanks: 1842 
The total discount needs to exceed \$20, so the minimum total discount is \$22.5, which is 9 times \$2.5. Hence the school must bring a minimum of 64 students. 
October 8th, 2018, 05:01 PM  #4 
Senior Member Joined: Apr 2017 From: New York Posts: 119 Thanks: 6 
so with fixed typo what is the inequality equation i need to set up?

October 8th, 2018, 07:03 PM  #5 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,590 Thanks: 953 
n = number of students over 55 Equation: 65.5  2.5n =< 45 
October 9th, 2018, 01:32 AM  #6 
Global Moderator Joined: Dec 2006 Posts: 19,950 Thanks: 1842 
Rearranging that gives 2.5n $\small\geqslant$ 65.5  45 = 20.5.


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