document.write( "Question 965879: Taylor has 6.70$ in quarters and dimes. If the total number of coins in her wallet is 17 how many quarters does she have \n" ); document.write( "

Algebra.Com's Answer #590408 by Edwin McCravy(20067) $\"\"$ $\"About$

You can put this solution on YOUR website!
Taylor has 6.70$ in quarters and dimes. If the total number of coins in her wallet is 17 how many quarters does she have
\n" ); document.write( "

\r\n" );
document.write( "\r\n" );
document.write( "This problem has a typo.  I think the number of coins should be 37, \r\n" );
document.write( "certainly not 17. I'll first do it with 17 to show you that there can be \r\n" );
document.write( "no way to have $6.70 in quarters and dimes with only 17 coins.  If \r\n" );
document.write( "you think about it, you know that's not possible because if they were all\r\n" );
document.write( "quarters, 17 quarters is only $4.50\r\n" );
document.write( "\r\n" );
document.write( "Then below that I'll do it changing the 17 to 37.\r\n" );
document.write( "\r\n" );
document.write( "Let the number of quarters be x\r\n" );
document.write( "Then the number of dimes, using\r\n" );
document.write( "ONE PART = TOTAL MINUS OTHER PART,\r\n" );
document.write( "is 17-x.\r\n" );
document.write( "                      Value      Value\r\n" );
document.write( "Type       Number       of         of\r\n" );
document.write( " of          of        EACH       ALL\r\n" );
document.write( "coin        coins      coin      coins\r\n" );
document.write( "-------------------------------------------\r\n" );
document.write( "quarters      x        $0.25    $0.25x\r\n" );
document.write( "dimes      17-x        $0.10    $0.25(17-x)\r\n" );
document.write( "-------------------------------------------\r\n" );
document.write( "TOTALS       17       -----     $6.70\r\n" );
document.write( "\r\n" );
document.write( " The equation comes from the column on the right\r\n" );
document.write( "\r\n" );
document.write( "  \r\n" );
document.write( "\r\n" );
document.write( " 0.25x + 0.10(17-x) = 6.70\r\n" );
document.write( "\r\n" );
document.write( "Get rid of decimals by multiplying every term by 100\r\n" );
document.write( "\r\n" );
document.write( "     25x + 10(17-x) = 670\r\n" );
document.write( "\r\n" );
document.write( "    25x + 170 - 10x = 670\r\n" );
document.write( "\r\n" );
document.write( "          15x + 170 = 670\r\n" );
document.write( "\r\n" );
document.write( "               15x = 500\r\n" );
document.write( "\r\n" );
document.write( "                 x = 33.3333333 = the number of quarters \r\n" );
document.write( "\r\n" );
document.write( "The number of dimes is 17-x or 17-33.3333333 or -16.3333333 dimes\r\n" );
document.write( "\r\n" );
document.write( "You cannot have a fraction number of quarters and a negative number\r\n" );
document.write( "of dimes.  There is no solution.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "-------------------------------------------------------\r\n" );
document.write( "\r\n" );
document.write( "Now here's the same problem using 37 coins instead of 17 coins.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Let the number of quarter be x\r\n" );
document.write( "Then the number of dime, using\r\n" );
document.write( "ONE PART = TOTAL MINUS OTHER PART,\r\n" );
document.write( "is 37-x.\r\n" );
document.write( "                      Value      Value\r\n" );
document.write( "Type       Number       of         of\r\n" );
document.write( " of          of        EACH       ALL\r\n" );
document.write( "coin        coins      coin      coins\r\n" );
document.write( "-------------------------------------------\r\n" );
document.write( "quarter      x         $0.25     $0.25x\r\n" );
document.write( "dime      37-x         $0.1      $0.1(37-x)\r\n" );
document.write( "-------------------------------------------\r\n" );
document.write( "TOTALS      37        -----      $6.70\r\n" );
document.write( "\r\n" );
document.write( " The equation comes from the column on the right\r\n" );
document.write( "\r\n" );
document.write( "  \r\n" );
document.write( "\r\n" );
document.write( "0.25x + 0.10(37-x) = 6.70\r\n" );
document.write( "\r\n" );
document.write( "Get rid of decimals by multiplying every term by 100\r\n" );
document.write( "\r\n" );
document.write( "     25x + 10(37-x) = 670\r\n" );
document.write( "\r\n" );
document.write( "    25x + 370 - 10x = 670\r\n" );
document.write( "\r\n" );
document.write( "          15x + 370 = 670\r\n" );
document.write( "\r\n" );
document.write( "               15x = 300\r\n" );
document.write( "\r\n" );
document.write( "                 x = 20 = the number of quarters\r\n" );
document.write( "\r\n" );
document.write( "The number of dimes is 37-x or 37-20 or 17 dimes\r\n" );
document.write( "\r\n" );
document.write( "Edwin

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

\n" );