c. How many pretzels must they sell to break even, according to the algebraic model?

b. If the income from selling the pretzels was $261, how many pretzels did they sell?

c. How many pretzels must they sell to break even, according to the algebraic model?

c. How many pretzels must they sell to break even, according to the algebraic model?

**Answer:**

*a) The cost of producing 40 pretzels is $656*

*The income for selling 40 pretzels is $116*

*b) They sold 90 pretzels*

*c) They must sell 240 pretzels to break-even*

**Step-by-step explanation:**

__Linear Models__

A linear model is an equation that describes a relationship between two quantities that have a constant rate of change.

One of the most-used equations of linear models is the slope-intercept form, written as:

y = mx + b

Where m is the slope of the graph of the line and b is the y-intercept.

The total cost of producing soft pretzels is divided into two parts:

* A fixed cost of $648 to set up their stand for the entire regatta.

* A variable cost of $0.20 per each pretzel.

Thus, the cost function can be written as:

C(x)=648+0.20x

Where x is the number of pretzels produced.

The students sell each pretzel for $2.90. This means the income (revenue) function for selling x pretzels is:

R(x)=2.90x

a) The cost of producing x=40 pretzels is:

C(40)=648+0.20*40

C(40)=648+8

C(40)=656

**The cost of producing 40 pretzels is $656**

The income is:

R(40)=2.90*40=116

**The income for selling 40 pretzels is $116**

b) If the income from selling pretzels is R=$261, then:

2.90x=261

Solving for x:

x = 261/2.90

x = 90

**They sold 90 pretzels**

c) To break-even the total cost and the income must be equal:

2.90x=648+0.20x

Subtraction 0.20x:

2.70x=648

Dividing by 2.70:

x = 648/2.70

x = 240

**They must sell 240 pretzels to break-even**

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