Question 1103213
Let {{{ n }}} = the original number of members that went
{{{ 2000/( n -5 ) = 2000/n + 20 }}}
Multiply both sides by {{{ n*( n - 5 ) }}}
{{{ 2000n = 2000*( n - 5 ) + 20*n*( n - 5 ) }}}
{{{ 2000n = 2000n - 10000 + 20n^2 - 100n }}}
{{{ 20n^2 - 100n - 10000 = 0 }}}
{{{ n^2 - 5n - 500 = 0 }}}
{{{ n = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{ a = 1 }}}
{{{ b =-5 }}}
{{{ c = -500 }}}
{{{ n = (-(-5) +- sqrt( (-5)^2-4*1*(-500) ))/(2*1) }}}
{{{ n = ( 5 +- sqrt( 25 + 2000 ) ) / 2 }}}
{{{ n = ( 5 + sqrt( 2025 ) ) / 2 }}}
{{{ n = ( 5 + 45 )/2 }}}
{{{ n = 25 }}}
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{{{ 25 - 5 = 20 }}}, so
20 people went on the expedition
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check:
{{{ 2000/( n-5 ) = 2000/n + 20 }}}
{{{ 2000/20 = 2000/25 + 20 }}}
{{{ 100 = 80 + 20 }}}
{{{ 100 = 100 }}}
OK