Two different catalogs

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Acecustis

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Company X is deciding between two different catalogs to customers. One catalog costs $0.50 to produce, is 50 pages long, has a 5% conversion rate, and the average converted customer brings in $315. The second catalog costs $0.95 to produce, is 100 pages long, and a converted customer brings in $300. What does the conversion rate of the second catalog need to be in order to make the same amount of profit as the first catalog? The profit margin is 30%.

Seems like simple Algebra, but I'm pretty lost on the setup. Any help?
 
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Certainly. Conversion rate in this case is how often a catalog led to an order/sale. So in our case, let's say we sent out 100 of the 1st catalog, the conversion rate was 5%. Meaning that 5 of the 100 catalogs led to a sale.

I believe I have solved the answer but please feel free to check my math.

Assumption: 100 catalogs of each are made.

Catalog 1
Costs = 100 * $0.50 = $50
Total Rev = 5 * $315 = $1575 (The 5 comes from 5% conversion rate for 100 catalogs, so 5 catalogs led to a sale)
Profit = 1575 - 50 = 1525

Catalog 2
Costs = 100 * $0.95 = $95
Total Rev = 300x (x will be the number of catalogs that led to a sale or conversion rate)
Total Profit = 300x - 95 = 1525
x = 5.4%

Does this make sense?
 
I think you are failing to take into account the 30% profit margin. How does your book define “profit margin,” relative to revenue or to cost of goods sold?
 
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