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