Question

Ginny wants to join a local dance club that has dance events every week. There are two membership options available: Ginny may become a premier member by paying a fee of $150 per year and attend an unlimited number of dances. Ginny may become a regular member by paying a fee of $50 and then pay $8 per dance she attends. How many dances must Ginny attend such that becoming a premier member will cost less, over the year, than becoming a regular member? Enter the answer in the box.

Answer 1

Explanation:

Premier membership: $150 per year

Regular membership: $50 per year + $8 per dance

The amount of dances Ginny should attend such that becoming a premier member cost less can be found by finding how many dances will cost her $150:

The regular membership can be model by:

$y=8x+50$

Where x is the amount of dances per year. We want to know x when y = 150:

$\begin{gathered} 150=8x+50 \\ 150-50=8x \\ x=\frac{150-50}{8}=12.5 \end{gathered}$

Since x is an amount of dances it cannot be 12.5 -one can't attend to 12 and a half dance-. With x = 12.5 Ginny would spend exactly $150. If she'd attend to 12 dances she would spend less than $150 and if she'd attend to 13 dances she would spend more.

Answer:

Ginny must attend to 13 dances or more such that becoming a premier member costs less.