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Josh, the manager of a bookstore cafe, is comleting his

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joemama142000
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Josh, the manager of a bookstore cafe, is comleting his [#permalink] New post   02 Dec 2005, 20:46
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Josh, the manager of a bookstore cafe, is comleting his weekly sales summary. Each customer bought either a cappaccino or a juice and the cafe sold 50% more juice than cappaccino. 1/3 of the customers who did not buy a cappaccino also bought a brownie and 3/4 of the total customers bought a bagel. If the number of bagels sold was 300 more than three times the number of brownies, how many customers did Josh's cafe serve?



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Re: Josh, the manager of a bookstore cafe, is comleting his [#permalink] New post   02 Dec 2005, 21:28
joemama142000 wrote:
Josh, the manager of a bookstore cafe, is comleting his weekly sales summary. Each customer bought either a cappaccino or a juice and the cafe sold 50% more juice than cappaccino. 1/3 of the customers who did not buy a cappaccino also bought a brownie and 3/4 of the total customers bought a bagel. If the number of bagels sold was 300 more than three times the number of brownies, how many customers did Josh's cafe serve?


From the stem, we are given the following information.
-----------------------------------------------------------------------------------
Bagles customer = 300 + 3 * Brownies = (3/4) * Total customers
Brownies customer = (1/3) * (Total customers - Cappuccino customers)
Juice customers = (3/2) * Cappuccino customers
Total customers = Juice customers + Cappuccino customers
-----------------------------------------------------------------------------------


Now we do the math.
-----------------------------------------------------------------------------------
Total customers = 400 + 4 * Brownies
= 400 + 4 * ( (1/3) * (Total customers - Cappuccino customers) )
= 400 + (4/3)Total customers - (4/3)Cappuccino customers

(-1/3)Total customers = 400 - (4/3)Cappuccino customers
Total customers = 4 * Cappuccino customers - 1200

Total customers = 4 * (1/2)Juice customers - 1200
= 2 * Juice customers - 1200

Total customers = 2 * Juice customers - 1200
Total customers = Juice customers + Cappuccino customers
Juice customers = (3/2) * Cappuccino customers

Juice customers = 3600
Cappuccino customers = 2400
-----------------------------------------------------------------------------------

The total number of customers served at joemama142000's cafe is 6000.

Wow...this PS question is really difficult. Took me more than 5 minutes.
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Re: Josh, the manager of a bookstore cafe, is comleting his [#permalink] New post   02 Dec 2005, 21:36
assuming each customer bought a single browni/begal.

cap = c
juice = j =c+0.5c=1.5c

total = total = j+c = 2.5c

brownie, b = 1.5c/3 = c/2
begal = (2.5c)(3)/4=7.5c/4
300 = (7.5c/4) - 3(c)/2
1.5c=300x4
c = 800

j=1200
t = 2000
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Re: Josh, the manager of a bookstore cafe, is comleting his [#permalink] New post   02 Dec 2005, 21:49
Quote:
From the stem, we are given the following information.
-----------------------------------------------------------------------------------
Bagles customer = 300 + 3 * Brownies = (3/4) * Total customers
Brownies customer = (1/3) * (Total customers - Cappuccino customers)
Juice customers = (3/2) * Cappuccino customers
Total customers = Juice customers + Cappuccino customers
-----------------------------------------------------------------------------------
Juice customers = 3600
Cappuccino customers = 2400
-----------------------------------------------------------------------------------
The total number of customers = 6000.

from your calculation
begal = (3/4) 6000 = 4500
brownie = 1/3(6000-2400) = 1200

begal = 300 +3 (Brownie)=300+ 3(1200) = 3600

how do you show that : begal = 300+3(brownie)[/quote]
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Re: Josh, the manager of a bookstore cafe, is comleting his [#permalink] New post   03 Dec 2005, 05:12
HIMALAYA wrote:
Quote:
From the stem, we are given the following information.
-----------------------------------------------------------------------------------
Bagles customer = 300 + 3 * Brownies = (3/4) * Total customers
Brownies customer = (1/3) * (Total customers - Cappuccino customers)
Juice customers = (3/2) * Cappuccino customers
Total customers = Juice customers + Cappuccino customers
-----------------------------------------------------------------------------------
Juice customers = 3600
Cappuccino customers = 2400
-----------------------------------------------------------------------------------
The total number of customers = 6000.

from your calculation
begal = (3/4) 6000 = 4500
brownie = 1/3(6000-2400) = 1200

begal = 300 +3 (Brownie)=300+ 3(1200) = 3600

how do you show that : begal = 300+3(brownie)
[/quote]

You are right. I must have made a mistake... :oops:



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Re: Josh, the manager of a bookstore cafe, is comleting his [#permalink]
03 Dec 2005, 05:12
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