document.write( "Question 1017226: A man has 30 coins in his pocket, all of which are dimes and quarters. If the total value of his change is 465 cents, how many dimes and how many quarters does he have? \n" ); document.write( "

Algebra.Com's Answer #633564 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!

\r\n" );
document.write( "Let the number of dimes be x\r\n" );
document.write( "Let the number of quarters be y\r\n" );
document.write( "\r\n" );
document.write( "\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( "dimes         x      $0.10     $0.10x\r\n" );
document.write( "quarters      y      $0.25     $0.25y\r\n" );
document.write( "-------------------------------------------\r\n" );
document.write( "TOTALS       30      -----     $4.65\r\n" );
document.write( "\r\n" );
document.write( " The first equation comes from the second column.\r\n" );
document.write( "\r\n" );
document.write( "  \r\n" );
document.write( "\r\n" );
document.write( "                   x + y = 30\r\n" );
document.write( "\r\n" );
document.write( " The second equation comes from the last column.\r\n" );
document.write( "  \r\n" );
document.write( "\r\n" );
document.write( "           0.1x + 0.25y = 4.65\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( "              10x + 25y = 465\r\n" );
document.write( "\r\n" );
document.write( " So we have the system of equations:\r\n" );
document.write( "           .\r\n" );
document.write( "\r\n" );
document.write( "We solve by substitution.  Solve the first equation for y:\r\n" );
document.write( "\r\n" );
document.write( "              x + y = 30\r\n" );
document.write( "                  y = 30 - x\r\n" );
document.write( "\r\n" );
document.write( "Substitute (30 - x) for y in 10x + 25y = 465\r\n" );
document.write( "\r\n" );
document.write( "   10x + 25(30 - x) = 465\r\n" );
document.write( "    10x + 750 - 25x = 465\r\n" );
document.write( "         -15x + 750 = 465\r\n" );
document.write( "               -15x = -285\r\n" );
document.write( "                  x = 19 = the number of dimes.\r\n" );
document.write( "\r\n" );
document.write( "Substitute in y = 30 - x\r\n" );
document.write( "              y = 30 - (19\r\n" );
document.write( "              y = 11 quarters.\r\n" );
document.write( "\r\n" );
document.write( "Checking:  19 dimes is $1.90 and 11 quarters is $2.75\r\n" );
document.write( "            That's 30 coins.\r\n" );
document.write( "            And indeed $1.90 + $2.75 = $4.65\r\n" );
document.write( "Edwin

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

\n" );