Question

Julianne opens a dance studio. Her start-up costs for the building, advertising, and supplies $52,000. Each day, she spends $650 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 a profit? Show all the work you did to arrive at your answer.

Answer:

Answer 1

The equation is:
`960d-650d=52000` and Julianne will begin making a profit after 168 days.

Step-by-step explanation

Her total start-up cost is $52,000.

Each day, she spends $650 on operating costs (like utilities and wages) and she earns $960 per day from her students' lesson fees.

If the number of days to overcome the start-up cost is
`d` , then

the total operation cost spent in
`d` days
`= \$650d` and

the total students' lesson fees earned in
`d` days
`= \$960d`

Part A: The equation to represent the situation will be:
`960d-650d=52000`

Part B: Julianne will begin making a profit when....

`960d-650d>52000\\ \\ 310d>52000\\ \\ d>(52000)/(310)\\ \\ d >167.741... \approx 168`

So, Julianne will begin making a profit after 168 days.