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A lemonade stand sold only small and large cups of lemonade on Tuesday

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A lemonade stand sold only small and large cups of lemonade on Tuesday  [#permalink]

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New post 23 Jan 2010, 14:17
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Question Stats:

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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

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-lemonade-stand-sold-only-small-and-large-cups-of-lemonade-123775.html
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Re: A lemonade stand sold only small and large cups of lemonade on Tuesday  [#permalink]

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New post 23 Jan 2010, 17:25
Snowingreen 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

disclaimer : each large cups costs 7/6 as much as small cups.



30 small sold.
20 large sold.

$1 for a small cup.

$30 for small.
20*7/6 for the large.

70/3 / (30+70/3)
= 70/3 / 160/3
=70/160
=7/16
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Re: A lemonade stand sold only small and large cups of lemonade on Tuesday  [#permalink]

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New post 24 Jan 2010, 10:21
A simpler way i guess would be to think that in total 5 cups were sold. Out of which 3 are small and 2 are large. Now let the small ones cost $6. so the large ones would cost $7.

So,
3*6=18 and 2*7=14.
Total revenue was 18+14=32
and Large cup sales as found above is 14
Therefore answer is 14/32 i.e 7/16
(a)
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Re: A lemonade stand sold only small and large cups of lemonade on Tuesday  [#permalink]

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New post 20 Feb 2010, 02:33
(2/5*7/6)/((3/5*1)+(2/5*7/6)) = 7/16 (A)
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Re: A lemonade stand sold only small and large cups of lemonade on Tuesday  [#permalink]

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New post 20 Feb 2010, 07:52
Snowingreen 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

disclaimer : each large cups costs 7/6 as much as small cups.


x - cost for small cup

y - total of large and small cups
Fraction = ((2/5)y * (7/6)x)/(xy(3/5+(2/5)*(7/6))) = 7/16 hence A.
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Re: A lemonade stand sold only small and large cups of lemonade on Tuesday  [#permalink]

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New post 20 Feb 2010, 08:49
(2*7)/(3*6) + (2*7)=14/ 18+14 = 14/32 = 7/16
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Re: A lemonade stand sold only small and large cups of lemonade on Tuesday  [#permalink]

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New post 22 Feb 2010, 08:07
5 cups total.

3 small cups sold
2 large cups sold

$6 each small cup
$7 each large cup

(3 small cups)($6) = $18
(2 small cups)($7) = $14

Proportional renevue from large cups = Revenue from large cups / Total revenue

14/32 = 7/16...

A is the right answer

Salud! :lol:
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Re: A lemonade stand sold only small and large cups of lemonade on Tuesday  [#permalink]

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New post 24 Jun 2016, 15:48
macsin wrote:
A simpler way i guess would be to think that in total 5 cups were sold. Out of which 3 are small and 2 are large. Now let the small ones cost $6. so the large ones would cost $7.

So,
3*6=18 and 2*7=14.
Total revenue was 18+14=32
and Large cup sales as found above is 14
Therefore answer is 14/32 i.e 7/16
(a)



Can you elaborate as to why you chose to use $6 and 7$?
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Re: A lemonade stand sold only small and large cups of lemonade on Tuesday  [#permalink]

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New post 25 Jun 2016, 01:36
Snowingreen 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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-lemonade-stand-sold-only-small-and-large-cups-of-lemonade-123775.html
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Re: A lemonade stand sold only small and large cups of lemonade on Tuesday   [#permalink] 25 Jun 2016, 01:36

A lemonade stand sold only small and large cups of lemonade on Tuesday

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