Serving Size, Price and Revenue

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On Wednesday, a restaurant sold a quantity of wine in 6 ounce servings, and on Thursday, it sold the same total quantity of wine in 4 ounce servings. If the price on Wednesday was $9.00 per glass, and the revenue on Thursday was that of the revenue on Wednesday, what was the price per glass of the wine on Thursday?

Review: Serving Size, Price and Revenue


Explanation

A lot of pieces of information are floating around in this question: revenue, glasses, prices. We can relate them in that revenue will be the number of glasses times the price:



And we have a relationship between the revenue on the two days:



Putting in the fact that the price on Wednesday was $9, and isolating the price on Thursday, we get:



We have information to determine the number of glasses. Consider the case in which 24 ounces of wine was sold. The number of glasses would be 4 on Wednesday and 6 on Thursday, so the ratio of glasses sold is 2 to 3:



That indicates a price per glass on Thursday of $4.50.

We can double-check that this makes sense: if the number of glasses sold was 50% higher on Thursday, but the revenue was only 75%, then the price per glass would have to be much lower. Continuing with the case we discussed, if on Wednesday the number of glasses was 4, then the revenue would be . And the revenue on Wednesday would be for 6 glasses, so the price must be $4.50. Indeed, we could have solved the question this way straightaway. The correct answer is (B).


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