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.

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....

$960d-650d>52000\\ \\ 310d>52000\\ \\ d>\frac{52000}{310}\\ \\ d >167.741... \approx 168$

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