Question 861727
Call what she started with, w, for "whole amount she started with".  This is a number, but we do not know its value.


Try to form a step-wise process.  First part,{{{w-(1/3)w}}}.  Simplify this NOW.
{{{(2/3)w}}} is what she has.


Second part, {{{(2/3)w-(1/4)(2/3)w}}} is what she has when spent the second part.  Simplify this now.  LCD is 12, seeing denominators as factors being 4 and 3.  
{{{(2/3)w(4/4)-(1/4)(2/3)w}}}
{{{(8/12)w-(2/12)w}}}
{{{(6/12)w}}}
{{{(1/2)w}}}


Third part, spending one fifth of the current amount at the museum.
{{{(1/2)w-(1/5)(1/2)w}}}, and LCD is 10.

{{{(5/10)w-(1/10)w}}}
{{{(4/10)w}}}
{{{(2/5)w}}}
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Finally, we are told that this amount is $32.40; so we have
{{{(2/5)w=32.40}}}


How do you undo multiplication by a fraction?  Multiply by the reciprocal.  Do this to BOTH sides of the equation!  What happens to the left-side member?  What happens to the right-side member?