document.write( "Question 1030299: A merchant wishes to blend 200 pounds of coffee to be worth $3.20 per pound from two types of coffee; one is worth $3.00 per pound and the other is worth $3.25 per pound. How many pounds of each mixture should he use? \n" ); document.write( "
Algebra.Com's Answer #645172 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "Let the number of pounds of cheaper coffee be x\r\n" );
document.write( "Let the number of pounds of costlier coffee 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( "coffee     pounds     pound      pounds\r\n" );
document.write( "-------------------------------------------\r\n" );
document.write( "cheaper      x      $3.00       $3.00x\r\n" );
document.write( "costlier     y      $3.25       $3.25y\r\n" );
document.write( "-------------------------------------------------\r\n" );
document.write( "mixture     200     $3.20   200($3.20) = $640.00\r\n" );
document.write( "\r\n" );
document.write( " The first equation comes from the \"Number of pounds\" column.\r\n" );
document.write( "\r\n" );
document.write( "  \"%28matrix%286%2C1%2CNumber%2Cof%2Cpounds%2C+of%2Ccheaper%2Ccoffee%29%29\"\"%22%22%2B%22%22\"\"%28matrix%286%2C1%2CNumber%2Cof%2Cpounds%2Cof%2Ccostlier%2Ccoffee%29%29\"\"%22%22=%22%22\"\"%28matrix%287%2C1%2Ctotal%2Cnumber%2Cof%2Cpounds%2Cof%2Cmixture%2Ccoffee%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "                 x + y = 200\r\n" );
document.write( "\r\n" );
document.write( " The second equation comes from the last column.\r\n" );
document.write( "  \"%28matrix%285%2C1%2CValue%2Cof%2CALL%2Ccheaper%2Ccoffee+%29%29\"\"%22%22%2B%22%22\"\"%28matrix%285%2C1%2CValue%2Cof%2CALL%2Ccostlier%2Ccoffee%29%29\"\"%22%22=%22%22\"\"%28matrix%285%2C1%2CTotal%2Cvalue%2Cof%2CALL%2Ccoffee%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "           3.00x + 3.25y = 640.00\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( "             300x + 325y = 64000\r\n" );
document.write( "\r\n" );
document.write( " So we have the system of equations:\r\n" );
document.write( "           \"system%28x+%2B+y+=+200%2C300x+%2B+325y+=+64000%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 = 200\r\n" );
document.write( "               y = 200 - x\r\n" );
document.write( "\r\n" );
document.write( "Substitute (200 - x) for y in 300x + 325y = 64000\r\n" );
document.write( "\r\n" );
document.write( "    300x + 325(200 - x) = 64000\r\n" );
document.write( "    300x + 65000 - 325x = 64000\r\n" );
document.write( "           -25x + 65000 = 64000\r\n" );
document.write( "                   -25x = -1000\r\n" );
document.write( "                      x = 40 = the number of pounds of cheaper.\r\n" );
document.write( "\r\n" );
document.write( "Substitute in y = 200 - x\r\n" );
document.write( "              y = 200 - (40)\r\n" );
document.write( "              y = 160 pounds of costlier.\r\n" );
document.write( "\r\n" );
document.write( "Checking:  40 pounds of cheaper is $120.00 and 160 \r\n" );
document.write( "           pounds of costlier is $520.00\r\n" );
document.write( "           That's 200 pounds of mixed coffee.\r\n" );
document.write( "           And indeed $120.00 + $520.00 = $640.00\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );