We can restate this problem as:

$13 is what percent of $52?

First, lets call the percent we are looking for "p" or #p%#.

"Percent" or "%" means "out of 100" or "per 100", Therefore p% can be written as #p/100#.

When dealing with percents the word "of" means "times" or "to multiply".

Putting this altogether we can write this equation and solve for #p# while keeping the equation balanced:

#$13 = p/100 xx $52#

#$13 = ($52p)/100#

#$13 xx color(red)(100/($52)) = ($52p)/100 xx color(red)(100/($52))#

#($1300)/($52) = ($52p)/100 xx 100/($52)#

#(color(green)(cancel(color(black)($)))1300)/(color(green)(cancel(color(black)($)))52) = (color(blue)(cancel(color(black)($52)))p)/color(red)(cancel(color(black)(100))) xx color(red)(cancel(color(black)(100)))/(color(blue)(cancel(color(black)($52))))#

#1300/52 = p#

#25 = p#