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A lemonade stand sold only small and large cups of lemonade

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A lemonade stand sold only small and large cups of lemonade [#permalink] New post 25 Nov 2011, 14:09
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A lemonade stand sold only small and large cups of lemonade on Tuesday. 3/5 of the cups sold were small and the rest were large. If the large cups were sold for 7/6 as much as the small cups, what fraction of Tuesday's total revenue was from the sale of large cups?

A. 7/16
B. 7/15
C. 10/21
D. 17/35
E. 1/2
[Reveal] Spoiler: OA

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Last edited by Bunuel on 05 Feb 2012, 14:17, edited 1 time in total.
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Re: A lemonade stand sold only small and large cups of lemonade [#permalink] New post 05 Feb 2012, 14:27
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manalq8 wrote:
A lemonade stand sold only small and large cups of lemonade on Tuesday. 3/5 of the cups sold were small and the rest were large. If the large cups were sold for 7/6 as much as the small cups, what fraction of Tuesday's total revenue was from the sale of large cups?

A. 7/16
B. 7/15
C. 10/21
D. 17/35
E. 1/2


This problem is very good example how easy and quick plug-in method might be.

Let the total # of cups be 10.
# of small cups sold 3/5*10=6;
# of large cups sold 10-6=4;

Let the price of small cup be $6, then the price of larges cup would be 7/6*6=$7;

Revenue from small cups: 6*$6=$36;
Revenue from large cups cups: 4*$7=$28;

Fraction of total revenue from large cups: 28/(36+28)=7/16.

Answer: A.
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Re: A lemonade stand sold only small and large cups of lemonade [#permalink] New post 03 Oct 2014, 08:57
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A lemonade stand sold only small and large cups of lemonade [#permalink] New post 03 Oct 2014, 21:33
......................... Small .................... Large ............ Total

Sale .................... \(\frac{3x}{5}\) ..................... \(\frac{2x}{5}\) ................. x (Assume)

Price ..................... a .......................... \(\frac{7a}{6}\)

Required Fraction\(= \frac{\frac{2x}{5} * \frac{7a}{6}}{\frac{3xa}{5} + \frac{14xa}{6}} = \frac{14xa}{30} * \frac{30}{32xa} = \frac{7}{16}\)
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Re: A lemonade stand sold only small and large cups of lemonade [#permalink] New post 12 Nov 2014, 01:15
Let total no. of cups be x
Small cups ( 3/5 x) + Large Cups (2/5 x) = x

Let the price of small cups be y
then price of large cups be 7/6 y

Therefore required fraction = Price of large cups * no. of large cups / Price of large cups * no. of large cups + Price of small cups * no. of small cups

= 2/5 x * 7/6 y
2/5 x * 7/6 y + 3/5 x * y

= 7/15 xy
7/15 xy + 3/5 xy

= xy * 7/15
xy * 7/15 + 9/15

= 7/ 16

therefore answer is A
Re: A lemonade stand sold only small and large cups of lemonade   [#permalink] 12 Nov 2014, 01:15
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