SAT Question 181cc4d6: Ratios Rates Proportional Relationships And Units answer and explanation with Desmos solution

Choice A is correct. It's given that rectangle $A$ has length $15$ and width $w$. Therefore, the length-to-width ratio of rectangle $A$ is $15$ to $w$. It's also given that rectangle $B$ has length $20$ and the same length-to-width ratio as rectangle $A$. Let $x$ represent the width of rectangle $B$. The proportion $\frac{15}{w}=\frac{20}{x}$ can be used to solve for $x$ in terms of $w$. Multiplying both sides of this equation by $x$ yields $\frac{15x}{w}=20$, and then multiplying both sides of this equation by $w$ yields $15x=20w$. Dividing both sides of this equation by $15$ yields $x=\frac{20w}{15}$. Simplifying this fraction yields $x=\frac{4}{3}w$.