Math CentralQuandaries & Queries


Question from svetik, a student:

The best selling dessert at Chez Russell earns revenue of $5000 per week. During Restaurant Week, they are required to give a 10% discount on this dessert. Because the owner is a crook, he decides to mark up the price the week before Restaurant Week and then give the 10% discount off the marked up price. During the marked up week, they still sold the same amount of pieces as any prior week. However, they expect to sell 100 more pieces during restaurant week. If the revenue from this dessert is the same for the marked up week and restaurant week, what is the normal price of the dessert, rounded to the nearest cent?


Let x be the number of pieces sold in a normal week and $p the normal price. You know that

$p × x = $5000

During the marked up week the price was 1.10 × $p and the number of pieces sold was x.

During the Restaurant week the price was 0.90 × 1.10 × p and the number of pieces sold was x + 100.

Can you complete the problem now?

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