Question 637539
Let {{{ n }}} = the original number of residents
Let {{{ d }}} = the original cost/resident
(1) {{{ 1200000 = d*n }}} 
(2) {{{ 1200000 = ( d + 3 )*( n -225 ) }}}
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(2) {{{ 1200000 = d*n + 3n - 225d + 675 }}}
Substitute (1) into (2)
(2) {{{ 1200000 = 1200000 + 3n - 225c + 675 }}}
(2) {{{ 3n = 225d - 675 }}}
(2) {{{ n = 75d - 225 }}}
Substitute this back into (1)
(1) {{{ 1200000 = d*( 75c -225 )  }}} 
(1) {{{ 75d^2 - 225d -1200000 }}}
(1) {{{ d^2 - 3d - 16000 }}}
{{{ d = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{ a = 1 }}}
{{{ b = -3 }}}
{{{ c = -16000 }}}
{{{ d = (-(-3) +- sqrt( (-3)^2 - 4*1*(-16000) ))/(2*1) }}}
{{{ d = ( 3 +- sqrt( 9 + 64000 )) / 2 }}}
{{{ d = ( 3 +- sqrt(  64009 )) / 2 }}}
{{{ d = ( 3 + 253) / 2 }}}
{{{ d = 256/2 }}}
{{{ d = 128 }}}
{{{ d + 3 = 131 }}}
The revised cost/resident is $131
check:
(1) {{{ 1200000 = d*n }}} 
(1) {{{ n = 1200000 / 128 }}}
(1) {{{ n = 9375 }}}
and
(2) {{{ 1200000 = ( 128 + 3 )*( 9375 -225 ) }}}
(2) {{{ 1200000 = 131*9150 }}}
{2) {{{ 1200000 = 1198650 }}}
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This is close but a little off. Can you see where I
messed up?