Sarah operated her lemonade stand Monday through

Question

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?

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?

Bunuel · Accepted Answer

Sarah operated the stand Monday through Friday (5 days) over a two week period, thus she operated the stand for total of 10 days.

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?

A. $ 1.50
B. $ 1.88
C. $ 2.25
D. $ 2.50
E. $ 3.25

7 regular days --> sales = 7*32*x = 224x;
3 hot days --> sales = 3*32*(1.25x) = 120x;

Total sales = 224x+120x = 344x.
Total cost = 10*32*0.75 = 240.

Profit = 344x - 240 = 276 --> x=1.5.
1.25x=~1.88.

Answer: B.

Hope it's clear.

deepri0812 · Answer

The steps are time taking , thought the calculations are easy..It took me also close to 2 minutes

Asishp · Answer

Ok I am not getting the answer ... 1.50 .. How many days are you cobsidering 10 or 13 ?

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Asishp · Answer

But the OA says A .. Is it wrong ?

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Bunuel · Answer

Yes, OA is B. Edited.

Asishp · Answer

Thanks ... I also got the same answer ...

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mynhauzen · Answer

You can put it all in one formula:
276 = (32*7*p+32*3*1.25*p) - 75*10*32
276 = (224p + 120p) - 24000 (thats in cents, or $240)
276+240 = 344p
1.5=p
p*1.25=~1.8

thorinoakenshield · Answer

Hi,

Is there a quick way to calculate the following without a calculator:

(516/344)*1.25

TO

KarishmaB · Answer

\frac{516}{344} * \frac{5}{4}

516 is divisible by 4 so cancel it out with 4 in the denominator:
 \frac{129}{344} * 5

Even now, the numbers are big. Try to see if you have any other common factors: 129 = 3 * 43 
We see that 3 is not a factor of 344 (since 3+4+4= 11 which is not a factor of 3). 
Next check if 43 is a factor of 344. Note that 43*8 = 344 - brilliant!

The numbers have reduced to

\frac{3}{8} * 5 = \frac{15}{8}

KarishmaB · Answer

Total 10 days of sale - 3 hot, 7 regular

Total cost price = $(3/4) * 32 cups * 10 days = $240
Total profit = $276
Total selling price = 240 + 276 = 516

Say, x is the selling price on regular day

516 = 7*x*32 + 3*(5x/4)*32 = Revenue on Regular day + Revenue on Hot day
516/32 = 7x + 15x/4
129/8 = 43x/4

129/2*43 = x

3/2 = x

Selling price on hot day = (5/4)*(3/2) = 15/8 = 1.88

Answer (B)

law258 · Answer

Mon-Fri = 5 day work week

Hot Days: PH = PR +0.25PR = 1.25PR

Solution:
= 3{32(1.25PR)}+2{32(PR)} = $276
--> PR = 276/184 = $1.5 --> PH = 1.25PR --> PH = $1.88

B.

shashankism · Answer

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

Kinshook · Answer

Given: 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.

Asked: 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?

Let the price of 1 cup on a regular day be $x.
Price of 1 cup on a hotday = $1.25x

Total days = 10
Hot days = 3
Regular days = 7

Revenues = 7*32*x + 3*32*1.25x = 224x + 120x = $344x
Costs = 10*32*.75 = $240
Profits = 344x - 240 = 276
344x = 516
x = 516/344

Price of 1 cup on a hot day = 1.25x = 5*516/4*344 = $1.875

IMO B

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Sarah operated her lemonade stand Monday through

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