#### Answer

$n = 52$

#### Work Step by Step

1. Multiply by $57-n$ on both sides of the equation to remove the fractions:
$\frac{n}{57-n} = 10 + \frac{2}{57-n}$
$n= 10(57-n) + \frac{2(57-n)}{57-n}$
2. Cancel out $57-n$ to simplify:
$n= 10(57-n) + 2$
3. Expand and solve for $n$
$n = 570 - 10n + 2$
$n - 570 + 10n - 2=0 $
$11n - 572 = 0$
$11(n-52) = 0$
$n - 52 = 0$
$n = 52$