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.

_________________

Auge um Auge, Zahn um Zahn !