Plz with question below 73 points julianne opens a dance studio her start up costs for the building advertising and supplies total is 52,000. each day, she spends 680 on operating costs. she earns 960 per day from her students lessons fees part a write an equation or inequality to represent this situation. let d be the number of the days part b when will julianne begin making a profit show all work and how you got to your answer

Start up costs = $52,000

She spends $680 per day, so 680d ( 680 times number of days)

She earns $960 per day, so 960d

Part A:  To calculate the number of days until she makes a profit, multiply the operating expenses  per day and add to the start up costs. The amount she makes per day need to either be equal or greater than those costs:

960d ≥ 52000 + 680d

Part B:

960d ≥ 52000 + 680d

Subtract 680d from each side:

280d ≥ 52000

Divide both sides by 280:

d = 52000 / 280 = 185.7, round up to 188

It will take 188 days for her to see a profit.

Initial cash on hand : $200.00
Ticket cost : $87.96
T-shirt cost per piece: $30.00

The first thing Staci needs to do is to deduct the cost of the ticket from her money.

$200  - 87.96 = $112.04

Stacy has the extra amount of 112.04 to purchase t-shirts. Since, each t-shirt costs $30. To know the number of shirts she can buy, she must divide the difference by 30.

$112.04 / $30 = 3.73

Based from the quotient, Stacy can buy 3 t-shirts.

$30 * 3 = $90 total cost of the tshirts.

$112.04 - 90 = $22.04

After buying the ticket and 3 tshirts, Staci has an excess of $22.04 from her $200.