Question 944261
Let {{{ n }}} = the original number of people
in the group
{{{ n + 2 }}} = The number when 2 people
join the group
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{{{ 575/n }}} = original cost/person
given:
{{{ 575/( n + 2 ) = 575/n - 2 }}}
Multiply both sides by {{{ n*( n+2 ) }}}
{{{ 575n = 575*( n+2 ) - 2n*( n+2 ) }}}
{{{ 575n = 575n + 1150 - 2n^2 - 4n }}}
{{{ 2n^2 + 4n - 1150 = 0 }}}
{{{ n^2 + 2n - 575 = 0 }}}
Use the quadratic formula
{{{ n = ( -b +- sqrt( b^2 - 4*a*c )) / (2*a) }}}
{{{ a = 1 }}}
{{{ b = 2 }}}
{{{ c = -575 }}}
{{{ n = ( -2 +- sqrt( 2^2 - 4*1*(-575) )) / (2*1) }}}
{{{ n = ( -2 +- sqrt( 4 + 2300 )) / 2 }}}
{{{ n = ( -2 +- sqrt( 2304 )) / 2 }}}
{{{ n = ( -2 + 47.96 ) / 2 }}}
{{{ n = 45.96/2 }}}
{{{ n = 22.98 }}}
23 people were in the original group
check:
{{{ 575/24.98 = 575/22.98 - 2 }}}
{{{ 23.02 = 25.02 - 2 }}}
{{{ 23.02 = 23.02 }}}
OK
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Normally {{{ n }}} would be a whole number, so
I don't know what happened. I think my equation
is OK, so check my math