Let's say the profit Marcus makes in x days is P (x) dollars.
Marcus earns $300 per day, so he earns $300 * x dollars in x days.
Marcus also pays a one-time rental fee of $400, so his total profit is: P (x) = 300x - 400.
Let's say the profit Lauren makes in x days is Q (x) dollars.
Lauren earns $250 per day, so she earns $250 * x dollars in x days.
Lauren also pays a one-time rental fee of $350, so her total profit is: Q (x) = 250x - 350.
The question asks when Marcus and Lauren make the same profit, so we need to find when P (x) = Q (x).
Therefore, 300x - 400 = 250x - 350.
We now need to solve this equation for x.
Marcus and Lauren each manage an ice cream parlor that is opening 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.
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