document.write( "Question 1025471: kevin and randy muise have a jar containing 79 coins, all of which are either quarters or nickels. the total value of the coins in the jar is 12.75 How many of each type of coins do they have?
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #640753 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!

\r\n" );
document.write( "Let the number of quarters be x\r\n" );
document.write( "Let the number of nickels be y\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( "quarters      x       $0.25      $0.25x\r\n" );
document.write( "nickels       y       $0.05      $0.05y\r\n" );
document.write( "-------------------------------------------\r\n" );
document.write( "TOTALS       79      -----       $12.75\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 = 79\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( "      0.25x + 0.05y = 12.75\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 + 5y = 1275\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( "\r\n" );
document.write( "We solve by substitution.  Solve the first equation for y:\r\n" );
document.write( "\r\n" );
document.write( "              x + y = 79\r\n" );
document.write( "                  y = 79 - x\r\n" );
document.write( " \r\n" );
document.write( "Substitute (79 - x) for y in 25x + 5y = 1275\r\n" );
document.write( "\r\n" );
document.write( "    25x + 5(79 - x) = 1275\r\n" );
document.write( "     25x + 395 - 5x = 1275\r\n" );
document.write( "          20x + 395 = 1275\r\n" );
document.write( "                20x = 880\r\n" );
document.write( "                  x = 44 = the number of quarters.\r\n" );
document.write( "\r\n" );
document.write( "Substitute in y = 79 - x\r\n" );
document.write( "              y = 79 - (44)\r\n" );
document.write( "              y = 35 nickels.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Checking:  44 quarters is $11.00 and 35 nickels is $1.75\r\n" );
document.write( "            That's 79 coins.\r\n" );
document.write( "            And indeed $11.00 + $1.75 = $12.75\r\n" );
document.write( "Edwin

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

\n" );