document.write( "Question 1189218: At a summer camp, each girl is assigned to one of 48 cabins that in total can accommodate 344 campers. There are two types of cabins-small ones that can house 6 girls and large ones that can house 10 girls. Last summer even though 344 girls had registered for the camp, only 342 could come. So one of the large cabins had only 8 girls. How many more small cabins are there than large cabins? \n" ); document.write( "

Algebra.Com's Answer #820519 by ikleyn(52777) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "At a summer camp, each girl is assigned to one of 48 cabins that in total can accommodate 344 campers.
\n" ); document.write( "There are two types of cabins-small ones that can house 6 girls and large ones that can house 10 girls.
\n" ); document.write( "Last summer even though 344 girls had registered for the camp, only 342 could come.
\n" ); document.write( "So one of the large cabins had only 8 girls. How many more small cabins are there than large cabins?
\n" ); document.write( "~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "L = the number of large cabins.\r\n" );
document.write( "\r\n" );
document.write( "(48-L) = the number of small cabins.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "From the condition, you have this equation\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    10*(L-1) + 8 + 6*(48-L) = 342\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Simplify and find L\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    10L - 10 + 8 + 6*48 - 6L = 342\r\n" );
document.write( "\r\n" );
document.write( "    4L = 342 + 10 - 8 - 6*48\r\n" );
document.write( "\r\n" );
document.write( "    4L = 56\r\n" );
document.write( "\r\n" );
document.write( "     L = 56/4 = 14.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "There were 14 large cabins and 48-14 = 34 small cabins.\r\n" );
document.write( "\r\n" );
document.write( "The number of small cabins was 20 more that the number of large cabins.    ANSWER\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "CHECK.  10*(14-1) + 8 + 6*34 = 342 girls, in total.    ! Correct !\r\n" );
document.write( "

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

\n" );