document.write( "Question 1034811: A jar of change contains 64 coins consisting only quarters and dimes. The total value of the coins in the jar $13.60. Let q= the number of quarters and d= the number of dimes. Writes two equations that describe the information given above. how many of each type of coin is in the jar?
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #649490 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!

\r\n" );
document.write( "Let the number of quarters be q\r\n" );
document.write( "Let the number of dimes be d\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( "quarters      q      $0.25       $0.25q\r\n" );
document.write( "dimes         d      $0.10       $0.10d\r\n" );
document.write( "-------------------------------------------\r\n" );
document.write( "TOTALS       64      -----       $13.60\r\n" );
document.write( "\r\n" );
document.write( " The first equation comes from the number of coins column.\r\n" );
document.write( "\r\n" );
document.write( "  \r\n" );
document.write( "                 q + d = 64\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( "           0.25q + 0.10d = 13.6\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( "              25q + 10d = 1360\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 d:\r\n" );
document.write( "\r\n" );
document.write( "             q + d = 64\r\n" );
document.write( "                 d = 64 - q\r\n" );
document.write( "\r\n" );
document.write( "Substitute (64 - q) for d in 25q + 10d = 1360\r\n" );
document.write( "\r\n" );
document.write( "    25q + 10(64 - q) = 1360\r\n" );
document.write( "     25q + 640 - 10q = 1360\r\n" );
document.write( "           15q + 640 = 1360\r\n" );
document.write( "                 15q = 720\r\n" );
document.write( "                   q = 48 = the number of quarters.\r\n" );
document.write( "\r\n" );
document.write( "Substitute in d = 64 - q\r\n" );
document.write( "              d = 64 - (48)\r\n" );
document.write( "              d = 16 dimes.\r\n" );
document.write( "\r\n" );
document.write( "Checking:  48 quarters is $12.00 and 16 dimes is $1.60\r\n" );
document.write( "            That's 64 coins.\r\n" );
document.write( "            And indeed $12.00 + $1.60 = $13.60\r\n" );
document.write( "Edwin

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

\n" );