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Carmen's Chocolates makes two varieties of chocolate bar. A Decadent Dark chocolate bar contains 4 oz of cocoa powder and 3 oz of sugar, while a Mellow Milk chocolate bar contains 2 oz of cocoa powder and 3 oz of sugar. Carmen has 120 oz of cocoa powder and 150 oz of sugar in stock. Decadent Dark bars sell for $6, while Mellow Milk bars sell for $2. What is the most money Carmen can make from selling chocolate bars, if she only uses the cocoa powder and sugar she has in stock?

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Answer:

US$ 180 is the most money Carmen can make after selling 30 bars of Decadent Dark chocolate

Step-by-step explanation:

1. Let's analyze all the data given to us to solve this case.

A. Decadent Dark chocolate

Amount of cocoa powder = 4 ounces

Amount of sugar = 3 ounces

Price = US$ 6

B. Mellow Milk chocolate

Amount of cocoa powder = 2 ounces

Amount of sugar = 3 ounces

Price = US$ 2

C. Stock

Amount of cocoa powder = 120 ounces

Amount of sugar = 150 ounces

2. What is the most money Carmen can make from selling chocolate bars, if she only uses the cocoa powder and sugar she has in stock?

Number of Decadent Dark chocolates Carmen can sell, according to the stock of ingredients:

Cocoa powder in stock = 120 ounces

Number of Decadent Dark chocolates Carmen can sell = Cocoa powder in stock/ Amount of Cocoa powder for each chocolate

Number of Decadent Dark chocolates Carmen can sell = 120/4

Number of Decadent Dark chocolates Carmen can sell = 30

Cocoa powder in stock after making 30 Decadent Dark chocolates = 0

Sugar in stock after making 30 Decadent Dark chocolates = 150 - (30 * 3)

Sugar in stock after making 30 Decadent Dark chocolates = 150 - 90

Sugar in stock after making 30 Decadent Dark chocolates = 60

Number of Mellow Milk chocolates Carmen can sell = Cocoa powder in stock/ Amount of Cocoa powder for each chocolate

Number of Decadent Dark chocolates Carmen can sell = 120/2

Number of Decadent Dark chocolates Carmen can sell = 60

Cocoa powder in stock after making 60 Mellow Milk chocolates = 0

However, sugar in stock for making 60 Mellow Milk chocolates is not enough = 150 - (60 * 3) = 150 - 180 = - 30

She would need 30 ounces of sugar more, so she just can make 50 Mellow Milk chocolate bars = 150/3 = 50

If Carmen makes 30 bars of Decadent Dark chocolate, she will sell US$ 180 (30 * 6), no cocoa powder will be left in stock and 60 ounces of sugar will remain.

If Carmen makes 50 bars of Mellow Milk chocolate, she will sell US$ 100 (50 * 2), 20 ounces of cocoa powder will be left in stock and no sugar will be left.

US$ 180 is the most money Carmen can make after selling 30 bars of Decadent Dark chocolate.

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