Question 1127044

let’s say  she has {{{x}}}

if she spends half her money in the first shop she visits, we have
she spend {{{x/2}}}

{{{x-x/2=x/2}}}=>remains

 in the second shop she spends {{{1/3}}} of what remains:
{{{(1/3)(x/2)=x/6}}}

in the third shop she spends ${{{25}}}

she then has ${{{15}}} left

she at the start {{{x}}} money and it should be equal to sum of all money she spent plus ${{{15}}} she has left

{{{x=x/2+x/6+25+15}}}......solve for {{{x}}}, both sides multiply by {{{6}}}

{{{6x=3x+x+150+90}}}

{{{6x=4x+240}}}

{{{6x-4x=240}}}

{{{2x=240}}}

{{{highlight(x=120)}}}


check:
in the first shop she  spend {{{x/2=120/2=60}}}
in the second shop she spends {{{x/6=120/6=20}}}  (or {{{(1/3)60=20}}})
in the third shop she spends ${{{25}}}
she then has ${{{15}}} 

add all together: {{{60+20+25+15=120}}}