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

Given: julianne  total startup cost = $52000

Operating cost per day =$680

Earn money from her lesson fee per day = $960

Find out the inequality of situation

Given d be the number of days

To proof: julianne spends on operating cost in d day = $680d

julianne earn from lesson fee in d day  = $960d

Total profit in d day = 960d-680d

Part A) Total profit should be greater than 52000. Because this is startup investment.

According to question inequality becomes

$960d-680d\geq52000$

Part B) Now solve for d

$280d\geq 52000$

$d\geq 185.7$

After 186 days, Julianne will get profit from dance studio.