document.write( "Question 1199189: A bus driver who starts with a large empty bus picks us 11 riders at every odd- numbered stop and drops off 5 riders at every even-numbered stop. The stop after which the bus will first contain more than 165 passengers is stop number
\n" ); document.write( " a) 27 b) 28 c) 52 d) 53 e) 55 \n" ); document.write( "

Algebra.Com's Answer #832919 by ikleyn(52794) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "A bus driver who starts with a large empty bus
\n" ); document.write( "picks us 11 riders at every odd-numbered stop and drops off 5 riders at every even-numbered stop.
\n" ); document.write( "The stop after which the bus will first contain more than 165 passengers is stop number
\n" ); document.write( "a) 27 b) 28 c) 52 d) 53 e) 55
\n" ); document.write( "~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "After the stop #2, there are   0 + (11-5)        =  6 riders in the bus.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "After the stop #4, there are   6 + (11-5) =  6+6 = 12 riders in the bus.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "After the stop #6, there are  12 + (11-5) = 12+6 = 18 riders in the bus.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "         As you can notice, there is a PATTERN: \r\n" );
document.write( "    after the stop #(2n), there are 6n riders in the bus.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Now,               165/6 = 27.5.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So, we expect the number n from this relation  n <~~~> 165/6 = 27.5,  \r\n" );
document.write( "which gives the number of the stop somewhere around  2n ~ 55.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Based on this estimation, let's look what happens  \r\n" );
document.write( "in vicinity of n= 27 (in vicinity of the stop #55).  \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "             See the table below.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    stop #      n       number of passengers \r\n" );
document.write( "                          after this stop \r\n" );
document.write( "  ---------------------------------------------\r\n" );
document.write( "\r\n" );
document.write( "      50       25         6*25     = 150             \r\n" );
document.write( "\r\n" );
document.write( "      51                  150 + 11 = 161             \r\n" );
document.write( "\r\n" );
document.write( "      52       26         6*26     = 156             \r\n" );
document.write( "\r\n" );
document.write( "      53                  156 + 11 = 167     <<<---=== here the number of passengers first time exceeded 165\r\n" );
document.write( "\r\n" );
document.write( "      54       27         6*27     = 162\r\n" );
document.write( "\r\n" );
document.write( "      55                  162 + 11 = 173   \r\n" );
document.write( "\r\n" );
document.write( "      56       28         6*28     = 168\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "From the table, you see that for the first time, the number of passengers will exceed 165 after stop #53.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "ANSWER.  For the first time, the number of passengers will exceed 165 after stop #53.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "------------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

This problem and my solution teaches you three key thing:

\r
\n" ); document.write( "\n" ); document.write( "         (a)   To organize your thoughts and calculations;\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "         (b)   To find a pattern;\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "         (c)   To make your logical conclusions based on estimations.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );