document.write( "Question 1206418: A shop owner paid a total of $2385 for some shirts and ties. Each shirt cost $14 less than each tie. The number of ties bought was 2/3 of the number of shirts bought. He paid $127.80 more for the ties than the shirts.\r
\n" ); document.write( "\n" ); document.write( "(a) How much did he pay for all the shirts?
\n" ); document.write( "(b) How many ties did he buy? \n" ); document.write( "

Algebra.Com's Answer #843882 by ikleyn(52800) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "A shop owner paid a total of $2385 for some shirts and ties.
\n" ); document.write( "Each shirt cost $14 less than each tie.
\n" ); document.write( "The number of ties bought was 2/3 of the number of shirts bought.
\n" ); document.write( "He paid $127.80 more for the ties than the shirts.
\n" ); document.write( "(a) How much did he pay for all the shirts?
\n" ); document.write( "(b) How many ties did he buy?
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "(a)  Let x be the amount he paid for all the shirts.\r\n" );
document.write( "\r\n" );
document.write( "     Then the amount which he paid for all the ties was by (x+127.80)  dollars.\r\n" );
document.write( "\r\n" );
document.write( "     An equation for the total is \r\n" );
document.write( "\r\n" );
document.write( "                 x + (x+127.80) = 2385  dollars.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     Simplify and find x\r\n" );
document.write( "\r\n" );
document.write( "           2x = 2385 - 127.80\r\n" );
document.write( "\r\n" );
document.write( "           2x = 2257.20\r\n" );
document.write( "\r\n" );
document.write( "            x = 2257.20/2 = 1128.60.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     Thus part (a) is solved.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "(b)  Let x be the number of shirts.\r\n" );
document.write( "\r\n" );
document.write( "     Then the number of ties is  .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     We just found in (a) the cost of all shirts. It is 1128.60 dollars.\r\n" );
document.write( "\r\n" );
document.write( "     Hence, the cost of all ties is  2385 - 1128.60 = 1256.40 dollars.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     The price of one shirt is then  .\r\n" );
document.write( "\r\n" );
document.write( "     The price for one tie  is   = .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     The difference of prices is 14 dollars (given).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     So, we write this \"price equation\"\r\n" );
document.write( "\r\n" );
document.write( "          -  = 14.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     Simplify and find x\r\n" );
document.write( "\r\n" );
document.write( "          = 14\r\n" );
document.write( "\r\n" );
document.write( "          = 14\r\n" );
document.write( "\r\n" );
document.write( "         x =  = 54.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     Thus the number of shirts was 54.\r\n" );
document.write( "\r\n" );
document.write( "     Then the number of ties was   = 36.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     At this point, part (b) is solved, too, and the ANSWER is 36 ties.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "The problem is solved in full ( = completely).\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );