The synergy show choir sold tickets to their latest performance. Students paid \(\$3.75\) per ticket, while adults paid \(\$6.00\) per ticket. They forgot to record the number of each type of ticket sold. They were excited that the show was sold out. That meant there were \(400\) people who came to the performance! The total money collected was \(\$1927.50\). How many of each type of ticket did they sell for their show?
Students: \(210\) tickets
Adults: \(190\) tickets