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:

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Sicista Sicista · Answer 1 · 2018-10-04T22:55:31+02:00

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

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 [tex]d[/tex] , then

the total operation cost spent in [tex]d[/tex] days [tex]= \$650d[/tex] and

the total students' lesson fees earned in [tex]d[/tex] days [tex]= \$960d[/tex]

Part A: The equation to represent the situation will be: [tex]960d-650d=52000[/tex]

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

[tex]960d-650d>52000\\ \\ 310d>52000\\ \\ d>\frac{52000}{310}\\ \\ d >167.741... \approx 168[/tex]

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