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.

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 (52000)/(310) =167.74 \approx168(ans)`