danzig wrote:

Sarah operated her lemonade stand Monday through Friday over a two week period and made a total profit of 276 dollars. On hot days she sold cups of lemonade for a price that was 25 percent higher than the regular days. Each cup she sold had a total cost of 75 cents and Sarah did not incur any other costs. If every day she sold exactly 32 cups and 3 of the days were hot, then what was the price of 1 cup on a hot day?

A. $ 1.50

B. $ 1.88

C. $ 2.25

D. $ 2.50

E. $ 3.25

The question is easy; I already solved it. However, it takes time to do it and many steps. Do you know a method to solve it in less tan 1.75 minutes?

In the two week period, Sarah operated lemonade for total 10 days out of which 3 were hot days and 7 were regular days.

Let p be the selling price on regular day and 1.25 p be the selling price on hot days.

So, 32*1.25*p*3 +32*p * 7 - 32*10 *0.75 = 276

-> 32p(3.75 + 7) = 276 + 320*0.75 = 276 +240 = 516

-> p = 516/32/10.75 = 129/8*10.75= 129/86 = 3/2 = 1.5

So, price of 1 cup on hot day = 1.5 *1.25 ~ 1.88

Answer B
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