A small theater with 200 seats sells two kinds of tickets for a performance. Premium tickets sell for $20 each and Standard tickets sell for $15 each. At a sold-out performance, $3400 was collected in ticket sales. How many tickets of each type were sold?

P + s = 200 ... p = 200 - s

20p + 15s = 3400

20 (200 - s) + 15s = 3400

4000 - 20s + 15s = 3400

-20s + 15s = 3400 - 4000

-5s = - 600

s = - 600/-5

s = 120 < = = = there were 120 standard tickets sold

p + s = 200

p + 120 = 200

p = 200 - 120

p = 80 < = = = there were 80 premium tickets sold