Chapter 4 - Proportions, Percents, and Solving Inequalities - 4.1 - Ratios and Proportions - Problem Set 4.1 - Page 149: 50

$n=45$

Using cross-multiplication, the value of the variable that satisfies the given equation, $ \dfrac{80-n}{n}=\dfrac{7}{9} ,$ is \begin{array}{l}\require{cancel} 9(80-n)=7n \\\\ 720-9n=7n \\\\ -9n-7n=-720 \\\\ -16n=-720 \\\\ n=\dfrac{-720}{-16} \\\\ n=45 .\end{array}