document.write( "Question 1004829: a bank teller counted P100 and P50 bills. this totaled to 117 bills worth P9950. how many bills of each type did she have? \n" ); document.write( "

Algebra.Com's Answer #621175 by Edwin McCravy(20056) $\"\"$ $\"About$

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document.write( "Let the number of P100's be x\r\n" );
document.write( "Let the number of P50's be y\r\n" );
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document.write( "                      Value      Value\r\n" );
document.write( "Type       Number       of         of\r\n" );
document.write( " of          of        EACH       ALL\r\n" );
document.write( "bill        bills      bill      bills\r\n" );
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document.write( "P100s        x        P100      P100x\r\n" );
document.write( "P50s         y         P50       P50y\r\n" );
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document.write( "TOTALS      117      -----      P9950\r\n" );
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document.write( " The first equation comes from the second column.\r\n" );
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document.write( "  \r\n" );
document.write( "                 x + y = 117\r\n" );
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document.write( " The second equation comes from the last column.\r\n" );
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document.write( "  \r\n" );
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document.write( "           100x + 50y = 9950\r\n" );
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document.write( " So we have the system of equations:\r\n" );
document.write( "           .\r\n" );
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document.write( "We solve by substitution.  Solve the first equation for y:\r\n" );
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document.write( "           x + y = 117\r\n" );
document.write( "               y = 117 - x\r\n" );
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document.write( "Substitute (117 - x) for y in 100x + 50y = 9950\r\n" );
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document.write( "   100x + 50(117 - x) = 9950\r\n" );
document.write( "    100x + 5850 - 50x = 9950\r\n" );
document.write( "           50x + 5850 = 9950\r\n" );
document.write( "                  50x = 4100\r\n" );
document.write( "                    x = 82 = the number of P100s.\r\n" );
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document.write( "Substitute in y = 117 - x\r\n" );
document.write( "              y = 117 - (82)\r\n" );
document.write( "              y = 35 P50s.\r\n" );
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document.write( "Checking:  82 P100s is P8200 and 35 P50s is P1750\r\n" );
document.write( "            That's 117 bills.\r\n" );
document.write( "            And indeed P8200 + P1750 = P9950\r\n" );
document.write( "Edwin

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