SAT Question 0e926898: Systems of Linear Equations answer and explanation with Desmos solution

Choice C is correct. It’s given that admission to the museum will cost $$8.50$ for each student and $$12$ for each chaperone. It's also given that it will cost a total of $$730$ for admission to the museum for all $83$ people on the field trip. Let $x$ represent the number of students and $y$ represent the number of chaperones going on the field trip. Since there are a total of $83$ people going on the field trip, it follows that $x+y=83$. Since admission to the museum for each student costs $$8.50$ and each chaperone costs $$12$, the total cost can be represented by the equation $8.50x+12y=730$. The equations $x+y=83$ and $8.50x+12y=730$ form a system of equations. Subtracting $x$ from both sides of the equation $x+y=83$ yields $y=83-x$. Substituting $83-x$ for $y$ in the equation $8.50x+12y=730$ yields $8.50x+12(83-x)=730$, or $-3.50x+996=730$. Subtracting $996$ from both sides of this equation yields $-3.50x=-266$. Dividing both sides of this equation by $-3.50$ yields $x=76$. Therefore, $76$ students are going on the field trip.