Julianne opens a dance studio. her start up costs for the building, advertising, and supplies total $52,000. each day, she spends $680 on operating costs (like utilities and wages). she earns $960 per day from her students' lesson fees. part a: write an equation or inequality to represent this situation. let d be the number of days. part b: when will julianne begin making profit? show all the work you did to arrive at your answer.

For this case we have:

Part A:

Since d is the variable that represents the number of days, we can represent an inequality for the gains given by:

Part B:

We want to know the moment from which Julianne obtains earnings, for that we clear d of the previous inequality:

To start making a profit, Julianne must work more than 186 days.

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below:

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