This case is about an opera house with declining profits and we are asked to calculate the revenue from single show, club member, and group discount ticket sales on Thursday-Sunday. After discovering Thursday is operating with an $1800 loss, we are asked to calculate what % of Thursday single ticket purchases would need to be converted to increase Thursday night traffic enough to break even?”

I understand we need to increase profit by $1800 to breakeven (30,000 costs- 28,200 revenues). The case simply divides $1800/80 [the price of a club ticket]. Why wouldn't we instead set up the problem this way: 

single ticket price * (volume -x) + club ticket price * (volume + x)= 1800

After solving for x, subtract x from the current number of single tickets sold (210) and divide that number by 210 to calculate the %.