A couple of college students get the idea to open a snack stand at the regatta festival this summer. The students sell delicious soft pretzels. They pay the city $648 to set up their stand for the entire regatta. They also figure the cost for dough, coarse salt, and other things they need is $0.20 per pretzel. They sell each pretzel for $2.90. a. What is the cost and the income obtained from selling forty pretzels? 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?

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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step-by-step explanation:

the camry sales+accord sale=828,000. to make it so the two numbers are 18 thousand apart and still equal 828,000, you first need to find out what half of 828,000 is. 828,000/2=414,000. for the two numbers to equal 828,000, you have to add the same amount as you subtract from the middle. in this case, the number is 9,000 because it's half of 18,000. to equal 828,000, you have to add 9,000 to 414,000 for the camry and subtract 9,000 from 414,000 for the accord. 414,000+9,000=423,000.

414,000-9,000=405,000.

423,000+405,000=828,000.

423,000-405,000=18,

hope it