Question 1205347
let the amount of money Belle has be {{{x}}}

if Alex had ${{{57}}} less than Belle, he has {{{x-57}}}

if Alex saved {{{3/5 }}}of his money , he saved {{{(3/5)(x-57)}}}=> so, he spent {{{(2/5)(x-57)}}}

if  Belle spent {{{2/3}}} of her money, she spent {{{(2/3)x}}}=>Belle’s savings is  {{{(1/3)x}}}

Given that the amount Alex spent was {{{1/4}}} of  Belles savings how much did Belle spend

{{{(2/5)(x-57)=(1/4)(1/3)x}}}
{{{(2x)/5 - 114/5 = x/12}}}
{{{(2x)/5 -x/12  =114/5 }}}
{{{(19x)/60  =114/5 }}}
{{{19x  =60(114/5) }}}
{{{19x  =1368}}}
{{{x  =1368/19}}}
{{{x  =72}}}


how much did Belle spend
answer: she spent : {{{(2/3)*72=48}}}


check:

Belle had ${{{72}}}=> she spent  {{{2/3}}} of her money ${{{(2/3)72=48}}} and saved ${{{72-48=24}}} 

Alex had ${{{72-57=15}}}=> he spent  {{{1/4}}} of  Belles savings which ${{{(1/4)24=6}}} and saved ${{{15-6=9}}}