SAT Question bf4a8b6a: Systems of Linear Equations answer and explanation with Desmos solution

Choice C is correct. Let $x$ represent the number of children in a whale-watching tour group. Let $y$ represent the number of adults in this group. Because it's given that $21$ people are in a group and the group consists of adults and children, it must be true that $x+y=21$. Since the company's revenue is $60$ dollars per child, the total revenue from $x$ children in this group was $60x$ dollars. Since the company's revenue is $80$ dollars per adult, the total revenue from $y$ adults in this group was $80y$ dollars. Because it's given that the total revenue for this group was $1,440$ dollars, it must be true that $60x+80y=1,440$. The equations $x+y=21$ and $60x+80y=1,440$ form a linear system of equations that can be solved to find the value of $x$, which represents the number of children in the group, using the elimination method. Multiplying both sides of the equation $x+y=21$ by $80$ yields $80x+80y=1,680$. Subtracting $60x+80y=1,440$ from $80x+80y=1,680$ yields $(80x+80y)-(60x+80y)=1,680-1,440$, which is equivalent to $80x-60x+80y-80y=240$, or $20x=240$. Dividing both sides of this equation by $20$ yields $x=12$. Therefore, $12$ people in the group were children.