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

Answer-

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

Solution-

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

Each day, she spends = $650,

and she earns = $960 per day,

If 'd' is the number of days to overcome the start-up and daily operation cost, then  

total operation cost of d days = $650d and  

total student lesson fees earned in d days = $960d

∴ The equation to represent the situation is,

$960d-650d = 52000$

∴ Julianne will begin making a profit,

$\Rightarrow 960d-650d \geq 52000$

$\Rightarrow 310d \geq 52000$

$\Rightarrow d \geq \frac{52000}{310} =167.74 \approx168(ans)$