Question

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.

Answer 1

For this case we have:

• Initial costs = $ 52,000

• Operating costs = $ 680 per day

• Earnings = $ 960 per day

Part A:

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

`680d + 52000 <960d\\`

Part B:

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

`52000 <960d-680d\\\\52000 <280d\\\\(52000)/(280)<d\\`

`185.7 <d\\\\d> 186 days\\`

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

Answer:

`680d + 52000 <960d\\\\d> 186 days\\\\`