# Chapter 4 - Proportions, Percents, and Solving Inequalities - 4.1 - Ratios and Proportions - Problem Set 4.1: 42

$n=5$

#### Work Step by Step

Using cross-multiplication, the value of the variable that satisfies the given equation, $\dfrac{5}{6}=\dfrac{n}{n+1} ,$ is \begin{array}{l}\require{cancel} 5(n+1)=6(n) \\\\ 5n+5=6n \\\\ 5n-6n=-5 \\\\ -n=-5 \\\\ n=5 .\end{array}

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