document.write( "Question 1054128: Barbara has some dimes and quarters. If she has 25 coins worth a total of $2.95, how many of each type of coin does she have? \n" ); document.write( "
Algebra.Com's Answer #669336 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       25      -----     $2.95\r\n" );
document.write( "\r\n" );
document.write( " The first equation comes from the second column.\r\n" );
document.write( "\r\n" );
document.write( "  \"%28matrix%283%2C1%2CNumber%2Cof%2Cdimes%29%29\"\"%22%22%2B%22%22\"\"%28matrix%283%2C1%2CNumber%2Cof%2Cquarters%29%29\"\"%22%22=%22%22\"\"%28matrix%284%2C1%2Ctotal%2Cnumber%2Cof%2Ccoins%29%29\"\r\n" );
document.write( "             \r\n" );
document.write( "                  x + y = 25\r\n" );
document.write( "\r\n" );
document.write( " The second equation comes from the last column.\r\n" );
document.write( "  \"%28matrix%284%2C1%2CValue%2Cof%2CALL%2Cdimes%29%29\"\"%22%22%2B%22%22\"\"%28matrix%284%2C1%2CValue%2Cof%2CALL%2Cquarters%29%29\"\"%22%22=%22%22\"\"%28matrix%285%2C1%2CTotal%2Cvalue%2Cof%2CALL%2Ccoins%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "          0.10x + 0.25y = 2.95\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 = 295\r\n" );
document.write( "\r\n" );
document.write( " So we have the system of equations:\r\n" );
document.write( "           \"system%28x+%2B+y+=+25%2C10x+%2B+25y+=+295%29\".\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 = 25\r\n" );
document.write( "                      y = 25 - x\r\n" );
document.write( "\r\n" );
document.write( "Substitute (25 - x) for y in 10x + 25y = 295\r\n" );
document.write( "\r\n" );
document.write( "       10x + 25(25 - x) = 295\r\n" );
document.write( "        10x + 625 - 25x = 295\r\n" );
document.write( "             -15x + 625 = 295\r\n" );
document.write( "                   -15x = -330\r\n" );
document.write( "                      x = 22 = the number of dimes.\r\n" );
document.write( "\r\n" );
document.write( "        Substitute in y = 25 - x\r\n" );
document.write( "                      y = 25 - (22)\r\n" );
document.write( "                      y = 3 quarters.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Checking:  22 dimes is $2.20 and 3 quarters is $0.75\r\n" );
document.write( "\r\n" );
document.write( "            That's 25 coins.\r\n" );
document.write( "\r\n" );
document.write( "And indeed $2.20 + $0.75 = $2.95\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );