SAT Question 17f176ec: Systems of Linear Equations answer and explanation with Desmos solution

Choice B is correct. The movie theater sells $f$ full-price tickets and $r$ reduced-price tickets, so the total number of tickets sold is $f+r$. Since the movie theater sold a total of $214$ full-price and reduced-price tickets for one movie showing, it follows that $f+r=214$. The movie theater charges $$11$ for each full-price ticket; thus, the sales for full-price tickets, in dollars, is given by $11f$. The movie theater charges $$8.25$ for each reduced-price ticket; thus, the sales for reduced-price tickets, in dollars, is given by $8.25r$. Therefore, the total sales, in dollars, for the movie showing is given by $11f+8.25r$. Since the total sales for all full-price and reduced-price tickets is $$2,145$, it follows that $11f+8.25r=2,145$.