Question 947102
Let {{{ x }}} = the original number
of passengers
----------------
At 1st stop:
{{{ x/2 }}} got off leaving
{{{ x/2 }}} of the passengers
{{{ 35 }}} boarded, so there are
{{{ x/2 + 35 }}} on the bus
-------------------------
At the 2nd stop,
{{{ (1/5)*( x/2 + 35 ) }}} got off the bus
{{{ (4/5)*( x/2 + 35 ) }}} are left on the bus
{{{ 40 }}} boarded, so there are
{{{ ( 4/5 )*( x/2 + 35 ) + 40 }}} on the bus
------------------------------------
there are now {{{ 80 }}} passengers on the bus, so
{{{ ( 4/5 )*( x/2 + 35 ) + 40 = 80 }}}
Multiply both sides by {{{ 5 }}}
{{{ 4*( x/2 + 35 ) + 200 = 400 }}}
Divide through by {{{ 4 }}}
{{{ x/2 + 35 + 50 = 100 }}}
{{{ x/2 = 15 }}}
{{{ x = 30 }}}
There were 30 passengers originally
check:
1/2 got off, so {{{ 30 - 15 = 15 }}}
left on bus. 35 boarded, so {{{ 15 + 35 = 50 }}}
now on bus
1/5 got off, {{{ 50 - 10 = 40 }}} left on bus
40 boarded, so {{{ 40 + 40 = 80 }}} are now on bus
OK