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You manage an ice cream factory that makes three flavors: Creamy Vanilla, Continental Mocha, and Succulent Strawberry. Into each batch of Creamy Vanilla go 2 eggs, I cup of milk, and 2 cups of cream. Into each batch of Continental Mocha go 1 egg, 1 cup of milk, and 2 cups of cream, while into each batch of Succulent Strawberry go 1 egg, 2 cups of milk, and 1 cup of cream. You have in stock 350 eggs, 350 cups of milk, and 400 cups of cream. How many batches of each flavor should you make in order to use up all of your ingredients

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elcharly64

Answer:

We must make 100 batches of Creamy Vanilla, 50 batches of Continental Mocha, and 100  batches of Succulent Strawberry

Step-by-step explanation:

System of Equations

The problem will be modeled as a system of three equations with 3 unknowns. Let's call the following variables

x=Number of batches of Creamy Vanilla ice creams

y=Number of batches of Continental Mocha ice creams

z=Number of batches of Succulent Strawberry ice creams

We know there are 350 eggs available and each Creamy Vanilla uses 2 eggs, each Continental Mocha uses 1 egg, and each Succulent Strawberry uses 1 egg. This condition leads to the equation:

(1)  [tex]2x+y+z=350[/tex]

Following the same reasoning, we set up the equation for the cups of milk

(2)  [tex]x+y+2z=350[/tex]

Finally, the ingredients for the Succulent Strawberry leads to the last equation

(3)  [tex]2x+2y+z=400[/tex]

The set of equations will be solved by the reduction method. Subtracting the equation (3) from the equation (1) we get

[tex]y=50[/tex]

Multiplying the equation (2) by -2 and adding to the equation (1)

[tex]-y-3z=-350[/tex]

solving for z

[tex]-3z=-350+y=-350+50[/tex]

[tex]z=100[/tex]

From equation (2)

[tex]x=350-y-2z=350-50-200[/tex]

[tex]x=100[/tex]

Thus, we must make 100 batches of Creamy Vanilla, 50 batches of Continental Mocha, and 100  batches of Succulent Strawberry

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