Chapter 4 - Proportions, Percents, and Solving Inequalities - 4.1 - Ratios and Proportions - Problem Set 4.1 - Page 149: 48

$n=75$

Using cross-multiplication, the value of the variable that satisfies the given equation, $ \dfrac{n}{200-n}=\dfrac{3}{5} ,$ is \begin{array}{l}\require{cancel} 5(n)=3(200-n) \\\\ 5n=600-3n \\\\ 5n+3n=600 \\\\ 8n=600 \\\\ n=\dfrac{600}{8} \\\\ n=75 .\end{array}