30 points explain the answer for both parts julianne opens a dance studio. her start-up costs for the building, advertising, and supplies total $52,000.each day, she spends $680 on operation costs (like utilities and wages). she earns 960$ 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 profit

A: $52,000 = D(-$680 + $960)

$52,000 is what Juli has to spend to get everything going. That is the number she has to hit before any money will be profit. Anything less than $52,000 is covering her startup costs.

Daily Juli has to also spend $680 so she is losing g money so it is negative. She is also gaining money from the business so the $960 is positive. Both amounts happen every day so both are multiplied by D (or number is days)

B: Juli is start making a profit on day 186

Solve for D by combining -$680 and $960 = $280
Juli will make $280 dollars every days after she pays her bills.

$52,000 = D($280)

We know how much we need ($52,000) and how much we will get every day ($280). Isolate D and divide 52,000 by 280.

52,000÷280=185.7142857143

185.7142857143 is greater than 185, so it will take Juli a min of 186 to make 52,000 and every $ after the $52,000 is now profit each day.

$280 per day for 186 days = $280 × 186 = $52,080

She will make $80 of profit on day 186