Question 936063
He bought the horses for $900 and made a profit of 
100%, so he sold the horses for $1800
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Let {{{ n + 1 }}} = the number of horses he bought
{{{ n }}} = the number of horses he sold
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The price he paid for each horse was:
{{{ 900 / ( n + 1 ) }}}
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The amount he received for each horse when he sold them was:
{{{ 1800 / n }}}
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His profit for each horse was:
{{{ 1800/n - 900/( n+1 ) = 110 }}}
Multiply both sides by {{{ n*( n+1 ) }}}
{{{ 1800*( n+1 ) - 900n = 110*n*( n+1 ) }}}
{{{ 1800n + 1800  - 900n = 110n^2 + 110n }}}
{{{ 110n^2 - 790n - 1800 = 0 }}}
{{{ 11n^2 - 79n - 180 = 0 }}}
Use the quadratic formula
{{{ n = ( -b +- sqrt( b^2 - 4*a*c )) / (2*a) }}}
{{{ a = 11 }}}
{{{ b = -79 }}}
{{{ c = -180 }}}
{{{ n = ( -(-79) +- sqrt( (-79)^2 - 4*11*(-180) )) / (2*11) }}}
{{{ n = ( 79 +- sqrt( 6241 + 7920 )) / 22 }}}
{{{ n = ( 79 +- sqrt( 14161 )) / 22 }}}
{{{ n = ( 79 + 119 ) / 22 }}}
{{{ n = 198/22 }}}
{{{ n = 9 }}}
{{{ n + 1 =10 }}}
He bought 10 horses
check:
{{{ 1800/n - 900/( n+1 ) = 110 }}}
{{{ 1800/9 - 900/( 9+1 ) = 110 }}}
{{{ 200 - 90 = 110 }}}
{{{ 110 = 110 }}}
OK