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 lulianne begin making a profit? Show all the work you did to arrive at your answer

Answer 1

`A - Inequality \ equation= 960d-680d > 52000`

`B -Julianne \ begin \ making \ a \ profit \ after \ 186 \ days`

Solution-

Julianne's start-up cost = $52,000

Daily operating costs = $680

Daily earnings = $960

And the number of days = d

The inequality that represents this situation,

`960d-680d > 52000`

⇒
`d(960-680)>52000`

In order to be in profit, she must surplus the initial investment and the daily expenses. The time taken by her to be in profit,

`d>(52000)/(960-680) > 185.71 \approx 186`

⇒
`d > 186 \ days`

∴ So after 186 days of starting the business, she will start making profits.