Question 1010767
Frank noticed that right now his dad, Peter, is five times older than his age.

{{{Peter = 5(frank)}}}.....eq.1

Last year (means current age minus {{{1}}}), Frank's age was half that of his brother, John. 
{{{Frank-1 = (1/2)(john-1)}}}
=>{{{Frank = (1/2)(john-1)+1}}}
=>{{{Frank = (1/2)john-1/2+1}}}
=>{{{Frank = (1/2)john+1/2}}}..........eq.2

Nine years from now (means current age plus {{{9}}}, Peter will be twice as old as John. 

{{{Peter+9 =2(john+9)}}}
=>{{{Peter=2(john+9)-9}}}

=>{{{Peter=2john+18-9}}}

=>{{{Peter=2john+9}}}.......eq.3


What is the sum of the current ages of Frank, John, and Peter?

from eq.1 and eq.3 we have

{{{ 5frank=2john+9}}}

{{{ frank=(2/5)john+9/5}}}.....eq.4

from eq.2 and eq.4 we have

{{{ (1/2)john+1/2=(2/5)john+9/5}}}.....solve for {{{john}}}

{{{ (john+1)/2=(2john+9)/5}}}.......cross multiply

{{{ 5(john+1)=2(2john+9)}}}

{{{ 5john+5=4john+18}}}

{{{ 5john-4john=18-5}}}

{{{ highlight(john=13)}}}


go to {{{ frank=(2/5)john+9/5}}}.....eq.4, substitute {{{13}}} for {{{john}}}

{{{ frank=(2/5)13+9/5}}}.....eq.4

{{{ frank=(26/5)+9/5}}}

{{{ frank=(26+9)/5}}}

{{{ frank=35/5}}}

{{{ highlight(frank=7)}}}

go to {{{Peter=2john+9}}}.......eq.3 , substitute {{{13}}} for {{{john}}}

{{{Peter=2*13+9}}}

{{{ highlight(Peter=35)}}}


so,  the sum of the current ages of Frank, John, and Peter is:

{{{ frank+john+peter=7+13+35=55}}}