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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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02 Dec 2005, 21:28
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joemama142000
From the stem, we are given the following information.
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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
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Now we do the math.
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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.
02 Dec 2005, 21:36
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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
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
