Question 891499
It sounds like they want you to find out the
rate at which students consume cookies
Over {{{ 10 }}} days, the rate is  {{{ c/3 }}} cookies / student
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The rate you want, though, is ( cookies / student ) / ( days to eat them )
{{{ ( c/s ) / 10 = c / ( 10s ) }}}
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Adding {{{ m }}} more students means you now have {{{ s + m }}} students
Let {{{ d }}} = the number of days for the {{{ s + m }}} students to
consume {{{ c }}} cookies
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You can set up the proportion:
( rate #1 ) = ( rate #2 )
{{{ c / ( 10s ) = c / ( d*( s + m ) ) }}}
Multiply both sides by {{{ 10s*( d*( s + m ) ) }}}
{{{ c*( d*( s + m ) ) = 10s*c }}}
Divide both sides by {{{ c }}}
{{{ d*( s + m ) = 10s }}}
{{{ d = ( 10s ) / ( s + m ) }}} answer
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Check:
Let {{{ c = 100 }}}
Let {{{ s = 20 }}}
Let {{{ m = 5 }}}
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{{{ ( c/s ) / 10 = c / ( 10s ) }}}
{{{ c / ( 10s ) = 100 / ( 10*20 ) }}}
{{{ c / ( 10s ) = 1/2 }}}
This is 1/2 a cookie per student per day
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If you add {{{ 5 }}} more students,
{{{ c / ( d*( s + m ) ) = 100 / ( d*( 20 + 5 ) ) }}}
{{{ c / ( d*( s + m ) ) = 100 / ( 25d ) }}}
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This is the same rate of eating, so
{{{ 1/2 = 100 / ( 25d ) }}}
{{{ 25d = 200 }}}
{{{ d = 8 }}}
So 25 students go through 100 cookies
in 8 days instead of 10- hope that's right