A gym offers regular memberships for $80 per month and off-peak memberships for $60 per month. Last month, the gym sold a total of 420 memberships for a total of $31,100. How many memberships sold were regular memberships?

Assume that the ticket number sold at a regular rate is x and the ticket number sold at concession is y.

The gym sold a total of 420 memberships, hence, x+y=420.

80x+60y=31100

20x+(60x+60y)=31100

20x+60(x+y)=31100

⇒20x+60*420=31100

20x+25200=31100

20x=31100−25200

20x=5900

x=295

While: x+y=420

=> 295+y=420

⇒y=420−295=125

Therefore, the ticket number sold at a regular rate is 295 and the ticket number sold at concession is 125.