Question 1160292

let number of cookies be  {{{x}}}

given:

He eats {{{1/4}}} of the package  on Monday
On Tuesday, he eats {{{13}}} cookies. 
On Wednesday, he eats {{{1/2}}} as many as he did on Monday=> {{{(1/4)/2=1/8}}}


so he ate:

{{{(1/4)x+13+(1/8)x}}}

. If there are {{{22 }}}cookies left in the package on Thursday, ->{{{x-22}}}

then we have

{{{(1/4)x+13+(1/8)x=x-22}}}

{{{(1/4)x+13+(1/8)x+22=x}}}......both sides multiply by {{{8}}}

{{{2x+104+ x+176=8x}}}

{{{280=8x-3x}}}

{{{5x=280}}}

{{{x=56}}}


 he start with {{{x=56}}} cookies

check:
he eats {{{(1/4)x=56/4=14}}}    on Monday
he eats {{{13}}} cookies on Tuesday
he eats {{{(1/8)x=56/8=7}}} on Wednesday
there are {{{22 }}}cookies left in the package on Thursday

add all together:
{{{14+13+7+22=56}}}
{{{56=56}}}