SAT Question 55ea82f3: Linear Inequalities answer and explanation with Desmos solution

Choice B is correct. It’s given that a team plans to sell at least $140$ tickets before an event and at least $220$ tickets during the event to raise a total of at least $$5,820$ from all tickets sold. It’s also given that the price of a ticket during the event is $$3$ less than the price of a ticket before the event and that $x$ represents the price, in dollars, of a ticket sold during the event. It follows that $x+3$ represents the price, in dollars, of a ticket sold before the event. The expression $140(x+3)$ represents the planned revenue, in dollars, from the tickets sold before the event, and the expression $220x$ represents the planned revenue, in dollars, from the tickets sold during the event. Thus, the expression $140(x+3)+220x$ represents the planned revenue, in dollars, from all tickets sold. Since the team plans to raise a total of at least $$5,820$ from all tickets sold, the total revenue must be at least $$5,820$. Therefore, the inequality $140(x+3)+220x\ge 5,820$ represents this situation.