Question 993318
Let {{{ n }}} = the number of pens
{{{ 400/n - 9 = 400/( n+9 ) }}}
Multiply both sides by {{{ n*( n+9 ) }}}
{{{ 400*( n+9 ) - 9*n*( n+9 ) = 400n }}}
{{{ 400n + 3600 - 9n^2 - 81n = 400n }}}
{{{ 9n^2 + 81n - 3600 = 0 }}}
{{{ n^2 + 9n - 400 = 0 }}}
Use quadratic formula
{{{ n = ( -b +- sqrt( b^2-4*a*c )) / (2*a) }}} 
{{{ a = 1 }}}
{{{ b = 9 }}}
{{{ c = -400 }}}
{{{ n = ( -9 +- sqrt( 9^2-4*1*(-400) )) / (2*1) }}} 
{{{ n = ( -9 +- sqrt( 81 + 1600 )) / 2 }}} 
{{{ n = ( -9 +- sqrt( 1681 )) / 2 }}} 
{{{ n = ( -9 + 41 ) / 2 }}}
{{{ n = 32/2 }}}
{{{ n = 16 }}}
The student bought 16 pens
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check:
{{{ 400/n - 9 = 400/( n+9 ) }}}
{{{ 400/16 - 9 = 400/( 16+9 ) }}}
{{{ 25 - 9 = 400/25 }}}
{{{ 16 = 16 }}}
OK