#### Answer

$n=\frac{3}{5}$

#### Work Step by Step

$\frac{n}{9}=\frac{n+1}{24}$ cross multiply
$24n=9(n+1)$ distributive property
$24n=9n+9$ subtract 9n from both sides
$24n-9n=9n+9-9n$ combine like terms
$15n=9$ divide both sides by 15
$15n\div15=9\div15$ simplify
$n=\frac{9}{15}$ reduce
$n=\frac{3}{5}$