SAT Question c5479c1a: Linear Equations In Two Variables answer and explanation with Desmos solution

Choice D is correct. It's given that the shipment consists of $5$ -pound boxes and $10$ -pound boxes with a total weight of $220$ pounds. Let $x$ represent the number of $5$ -pound boxes and $y$ represent the number of $10$ -pound boxes in the shipment. Therefore, the equation $5x+10y=220$ represents this situation. It's given that there are $13$

$10$ -pound boxes in the shipment. Substituting $13$ for $y$ in the equation $5x+10y=220$ yields $5x+10\left(13\right)=220$, or $5x+130=220$. Subtracting $130$ from both sides of this equation yields $5x=90$. Dividing both sides of this equation by $5$ yields $18$. Thus, there are $18$

$5$ -pound boxes in the shipment.