SAT Question 993000da: Percentages answer and explanation with Desmos solution

Choice D is correct. It's given that $a$ is $230\%$ of $b$. It follows that $a=\frac{230}{100}b$. It's also given that $a$ is $60\%$ of $c$. It follows that $a=\frac{60}{100}c$. Since $a=\frac{230}{100}b$ and $a=\frac{60}{100}c$, it follows that $\frac{230}{100}b=\frac{60}{100}c$. Multiplying each side of this equation by $\frac{100}{60}$ yields $\frac{23}{6}b=c$. If $c$ is $p\%$ of $b$, then $c=\frac{p}{100}b$. It follows that $\frac{23}{6}=\frac{p}{100}$. Multiplying each side of this equation by $100$ yields $\frac{2,300}{6}=p$. It follows that the value of $p$ is approximately $383.33$. Therefore, of the given choices, $383$ is closest to the value of $p$.