Question ACCA Dec 16

Dear Sir, I came across the following question (truncated text) from Dec 16 ACCA exam: Based on the prices it charges for entry to similar events in other locations, Hare Events has decided on an entry fee of $55 for the full marathon and $30 for the half marathon. It expects that the maximum entries will be 20,000 for the full marathon and 14,000 for the half marathon Variable costs: Full marathon Half marathon Race packs 15·80 10·80 Water stations 2·40 1·20 Fixed costs: Council fees 300,000 Risk assessment and insurance 50,000 Marketing 30,000 Photography 5,000 QUESTION Hare Events wishes to achieve a minimum total profit of $500,000 from the running festival. What are the number of entries Hare Events will have to sell for each race in order to achieve this level of profit, assuming a constant sales mix based on the expected race entry numbers applies? A Full marathon: 17,915 entries and half marathon: 12,540 entries B Full marathon: 14,562 entries and half marathon: 18,688 entries C Full marathon: 20,000 entries and half marathon: 8,278 entries D Full marathon: 9,500 entries and half marathon: 6,650 entries MY ANSWER I work with the C/S ratio and find expected revenue to achieve the profit of 500k is $1,361,538. Then I apportion based on the mix of 20,000 / 14,000 expected runners: Full marathon: $1,361,538/34,000*20,000/$55 = 14,561 runners Half marathon: $1,361,538/34,000*14,000/$30 = 18,688 runners ANSWER B However the correct answer is A: Weighted average C/S ratio = 65% Revenue to achieve target profit = $885,000/65% = $1,361,538 Marathon ($110/$152) x $1,361,538 = $985,324/$55 = 17,915 entries Half marathon ($42/$152) x $1,361,538 = $376,214/$30 = 12,540 entries I do not understand where the $100/$152 and $42/$100 come from. Could you please explain me why my reasoning is wrong? Many thanks for your help, Anne