Question 1196288



let the price of pack of pencils be {{{p}}} and the price of a pack of composition notebooks {{{n}}} 

if Olivia bought four composition notebooks and three packs of pencils from the school bookstore and paid ${{{10.93}}}, we have

{{{3p+4n=10.93}}}.............solve for {{{p}}}

{{{3p=10.93-4n}}}

{{{p=(10.93-4n)/3}}}.........eq.1

if Jackie bought seven composition notebooks and two packs of pencils and paid ${{{13.31}}}, we have

{{{2p+7n=13.31}}}.............solve for {{{p}}}

{{{2p=13.31-7n}}}

{{{p=(13.31-7n)/2}}}........eq.1

from  eq.1 and  eq.2 we have

{{{(10.93-4n)/3=(13.31-7n)/2}}}..........cross multiply

{{{2(10.93-4n)=3(13.31-7n)}}}

{{{21.86 - 8n=39.93 - 21n}}}..........solve for {{{n}}}

{{{21n - 8n=39.93 -21.86 }}}

{{{13n=18.07 }}}

{{{n=18.07/13 }}}

{{{n=1.39 }}}

go to  {{{p=(13.31-7n)/2}}}........eq.1, substitute {{{n=1.39 }}}

{{{p=(13.31-7*1.39)/2}}} 

{{{p=3.58/2}}} 

{{{p=1.79}}} 


so,  the price of a pack of pencils is {{{1.79}}}