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Sarah operated her lemonade stand Monday through

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Sarah operated her lemonade stand Monday through  [#permalink]

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New post 28 Dec 2012, 09:19
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Question Stats:

52% (03:19) correct 48% (03:39) wrong based on 233 sessions

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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?
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Re: Sarah operated her lemonade stand Monday through  [#permalink]

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New post 29 Dec 2012, 03:20
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?



The steps are time taking , thought the calculations are easy..It took me also close to 2 minutes
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Re: Sarah operated her lemonade stand Monday through  [#permalink]

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New post 28 May 2013, 10:02
Ok I am not getting the answer ... 1.50 .. How many days are you cobsidering 10 or 13 ?

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Re: Sarah operated her lemonade stand Monday through  [#permalink]

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New post 28 May 2013, 10:31
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Asishp wrote:
Ok I am not getting the answer ... 1.50 .. How many days are you cobsidering 10 or 13 ?

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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

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.
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Re: Sarah operated her lemonade stand Monday through  [#permalink]

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New post 28 May 2013, 11:42
But the OA says A .. Is it wrong ?

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Re: Sarah operated her lemonade stand Monday through  [#permalink]

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New post 28 May 2013, 12:26
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New post 28 May 2013, 12:31
Thanks ... I also got the same answer ...

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Re: Sarah operated her lemonade stand Monday through  [#permalink]

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New post 03 Nov 2013, 07:50
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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
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Re: Sarah operated her lemonade stand Monday through  [#permalink]

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New post 15 Jan 2015, 20:43
Bunuel wrote:
Asishp wrote:
Ok I am not getting the answer ... 1.50 .. How many days are you cobsidering 10 or 13 ?

Image Posted from GMAT ToolKit


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

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.


Hi,

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

(516/344)*1.25

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Re: Sarah operated her lemonade stand Monday through  [#permalink]

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New post 16 Jan 2015, 00:08
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thorinoakenshield wrote:

Hi,

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

(516/344)*1.25

TO


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

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

\(\frac{3}{8} * 5 = \frac{15}{8}\)
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Re: Sarah operated her lemonade stand Monday through  [#permalink]

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New post 16 Jan 2015, 01:18
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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?


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)
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Re: Sarah operated her lemonade stand Monday through  [#permalink]

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New post 27 Jan 2017, 15:43
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.
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Re: Sarah operated her lemonade stand Monday through  [#permalink]

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New post 14 Aug 2017, 02:50
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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Re: Sarah operated her lemonade stand Monday through &nbs [#permalink] 14 Aug 2017, 02:50
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