Question 758664
Let {{{ n }}} = the number of articles he bought
{{{ 540/n }}} = the cost / article that he bought
He lost 2, so he had {{{ n - 2 }}} left
He sold the rest at $6 per article more than he gave for them
{{{ 540/n + 6 }}} per item is what he sold {{{ n - 2 }}} items for
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He gained 10% overall
{{{ 540 + .1*540 = 594 }}}
He ended up with $594
{{{ ( 540/n + 6 )*( n - 2 ) = 594 }}}
{{{ 540 + 6n - 1080/n - 12 = 594 }}}
{{{ 6n = 594 - 528 + 1080/n }}}
{{{ 6n^2 = 66n + 1080 }}}
{{{ -n^2 + 11n + 180 = 0 }}}
Use quadratic formula
{{{ n = (-b +- sqrt( b^2 - 4*a*c )) / (2*a) }}}
{{{ a = -1 }}}
{{{ b = 11 }}}
{{{ c = 180 }}}
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{{{ n = (-11 +- sqrt( 11^2 - 4*(-1)*180 )) / (2*(-1)) }}}
{{{ n = (-11 +- sqrt( 121 + 720 )) / (-2) ) }}}
{{{ n = (-11 +- sqrt( 841 )) / (-2) ) }}}
{{{ n = (-11 +- 29) / (-2) ) }}}
{{{ n = ( -11 - 29 ) / (-2) }}}
{{{ n = 20 }}}
(Note that I can't use the (+) square root )
He bought 20 articles
check:
540/20 = 27
He lost 2 and had 18
{{{ 18*( 27 + 6 ) = 18*33 }}}
{{{ 18*33 = 594 }}}
This is 10% more that he paid originally
OK