SAT Question 71189542: Systems of Linear Equations answer and explanation with Desmos solution

Choice C is correct. Let $x$ represent the number of $2$-person tents and let $y$ represent the number of $4$-person tents. It is given that the total number of tents was $60$ and the total number of people in the group was $202$. This situation can be expressed as a system of two equations, $x+y=60$ and $2x+4y=202$. The first equation can be rewritten as $y=-x+60$. Substituting $-x+60$ for $y$ in the equation $2x+4y=202$ yields $2x+4\times (-x+60)=202$. Distributing and combining like terms gives $-2x+240=202$. Subtracting $240$ from both sides of $-2x+240=202$ and then dividing both sides by $-2$ gives $x=19$. Therefore, the number of $2$-person tents is $19$.

Alternate approach: If each of the $60$ tents held $4$ people, the total number of people that could be accommodated in tents would be $240$. However, the actual number of people who slept in tents was $202$. The difference of $38$ accounts for the $2$-person tents. Since each of these tents holds $2$ people fewer than a $4$-person tent, $\frac{38}{2}=19$ gives the number of $2$-person tents.