Question about Ross Case "Opera House" Math Problem

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 %.

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