Marcus and Lauren each manage an ice cream parlor that is open during the summer. Marcus pays a one-time rental fee of 400$ and earns an average of 300$ per day from ice cream sales. Lauren pays a one-time rental fee of 350$ and earns an average of 250$ per day from ice cream sales. How many days would it take Marcus and Lauren to earn the same amount of profit? Create an equation to model this equation where x represents the number of days.
Marcus's profit is given by the equation:
Profit = Income - Rental fee = 300x - 400
Lauren's profit is given by the equation:
Profit = Income - Rental fee = 250x - 350
To find the number of days it would take for Marcus and Lauren to earn the same amount of profit, we set their profit equations equal to each other and solve for x:
300x - 400 = 250x - 350
Subtract 250x from both sides:
50x - 400 = -350
Add 400 to both sides:
50x = 50
Divide both sides by 50:
x = 1
It would take Marcus and Lauren 1 day to earn the same amount of profit.