SAT Question b23bba4c: Linear Equations In Two Variables answer and explanation with Desmos solution

Choice A is incorrect. If the number of large boxes shipped is $3$, then $b=3$. Substituting $3$ for $b$ in the given equation yields $3a+4\times 3=25$ or $3a+12=25$. Subtracting $12$ from both sides of the equation and then dividing by $3$ yields $a=\frac{13}{3}$. However, it's given that the number of small boxes shipped, $a$, is $3$, not $\frac{13}{3}$, so $b$ cannot equal $3$.

Choice C is incorrect. If the number of large boxes shipped is $5$, then $b=5$. Substituting $5$ for $b$ in the given equation yields $3a+4\times 5=25$ or $3a+20=25$. Subtracting $20$ from both sides of the equation and then dividing by $3$ yields $a=\frac{5}{3}$. However, it's given that the number of small boxes shipped, $a$, is $3$, not $\frac{5}{3}$, so $b$ cannot equal $5$.

Choice D is incorrect. If the number of large boxes shipped is $6$, then $b=6$. Substituting $6$ for $b$ in the given equation yields $3a+4\times 6=25$ or $3a+24=25$. Subtracting $24$ from both sides of the equation and then dividing by $3$ yields $a=\frac{1}{3}$. However, it's given that the number of small boxes shipped, $a$, is $3$, not $\frac{1}{3}$, so $b$ cannot equal $6$.