Chapter 4 - Proportions, Percents, and Solving Inequalities - 4.1 - Ratios and Proportions - Problem Set 4.1 - Page 149: 41

$n=7$

Using cross-multiplication, the value of the variable that satisfies the given equation, $ \dfrac{n+1}{n}=\dfrac{8}{7} ,$ is \begin{array}{l}\require{cancel} 7(n+1)=8(n) \\\\ 7n+7=8n \\\\ 7n-8n=-7 \\\\ -n=-7 \\\\ n=7 .\end{array}