Kate is ordering cupcakes online for the party tonight. The Bakery prices cupcakes according to the number of cupcakes ordered. For orders of $20$ or fewer cupcakes, the price is $4.50$ dollars per cupcake plus $12$ dollars shipping and handling on the order. For orders of more than $20$ cupcakes, the additional cupcakes over $20$ will recieve a $20$\% discount. Given that Kate\textquotesingle s bill is $120$ dollars, how many cupcakes does she order? 
Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems in Economics->Segment Pricing