# Question about Ross Case "Opera House" Math Problem

case math McKinsey Practice cases
New answer on Oct 25, 2022
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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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Because it says, on slide 3, that the client believes the opportunity is to sell more club tickets… Given that, you are only focusing on that type of tickets thereafter.