Question 1011340

Alice has {{{50}}}%={{{1/2}}} of the amount of money Betty has,then Alice  has {{{1/2}}}  what Betty has

{{{Alice=(1/2)Betty}}}

and if Carrie has {{{2/5}}} of what Alice, then {{{Carrie=(2/5)Alice}}}

=>{{{Carrie/(2/5)=Alice}}}
=>{{{Alice=(5/2)Carrie}}}....eq.1

 If Betty has ${{{364}}} more than Carrie, then {{{Betty=Carrie+364}}}.

then {{{Alice=(1/2)Betty}}}=>{{{Alice=(1/2)(Carrie+364)}}}.......eq.2

from eq.1 and eq.2 we have:

{{{(5/2)Carrie=(1/2)(Carrie+364)}}}....both sides multiply by {{{2}}}
{{{5Carrie=Carrie+364}}}

{{{5Carrie-Carrie=364}}}

{{{4Carrie=364}}}

{{{Carrie=364/4}}}

{{{highlight(Carrie=91)}}}

then {{{Alice=(5/2)Carrie}}}....eq.1

{{{Alice=(5/2)91}}} 

{{{highlight(Alice=227.5)}}}

and {{{Alice=(1/2)Betty}}}

{{{Betty=2*Alice}}}

{{{Betty=2*227.5}}}

{{{highlight(Betty=455)}}}


check:

Alice has {{{50}}}%={{{1/2}}} of the amount of money Betty has: {{{455/2=227.5}}}

 {{{Betty=Carrie+364}}}=> {{{455=91+364}}}=> {{{455=455}}}

{{{Alice=(5/2)Carrie}}}=>{{{Alice=(5/2)91=227.5}}}