On your next vacation, you will divide lodging between large resorts and small inns. Let $x$ represent the number of nights spent in large resorts. Let $y$ represent the number of nights spent in small inns. Answer parts $($a$)-($c$).$

a$.$ Write a system of inequalities that models the following conditions.

You want to stay at least $8$ nights. At least one night should be spent at a large resort. Large resorts average $$100$ per night and small inns average $$50$ per night. Your budget permits no more than $$600$ for lodging.

Choose the correct system of inequalities below.

A$.x+y8,x1,y0,100x+50y600$

B$.x+y8,x1,y0,50x+100y600$

C$.x+y8,x0,y1,100x+50y600$

D$.x+y8,x1,y0,100x+50y600$

E$.x+y8,x0,y1,100x+50y600$

F$.x+y8,x1,y0,100x+50y600$

G$.x+y8,x0,y1,100x+50y600$

H$.x+y8,x0,y1,50x+100y600$