document.write( "Question 725740: A collection of 36 coins consist of dimes and nickles. The total value is $2.15. How many dimes are there \n" ); document.write( "

Algebra.Com's Answer #444265 by Edwin McCravy(20060) $\"\"$ $\"About$

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document.write( "Two ways to do it.\r\n" );
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document.write( "Without algebra:\r\n" );
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document.write( "It would take $2.15÷$0.05 = 43 nickels to make $2.15. We\r\n" );
document.write( "start with 43 nickels. But that is 43-36 or 7 coins too many.\r\n" );
document.write( "So we take away 7 nickels leaving 36 nickels.  Now to make up \r\n" );
document.write( "for those 7 nickels we took away, we replace 7 of those 36 \r\n" );
document.write( "nickels by dimes.  So we have 7 dimes and 36-7 or 29 nickels. \r\n" );
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document.write( "With algebra:\r\n" );
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document.write( "Let x = the number of dimes.\r\n" );
document.write( "Then the number of nickels is 36-x.\r\n" );
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document.write( "           coins    value per coin    value of coins   \r\n" );
document.write( "dimes        x           0.10             0.10x\r\n" );
document.write( "nickels    36-x          0.05          0.05(36-x)                 \r\n" );
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document.write( "total       36                            2.15\r\n" );
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document.write( "                  \r\n" );
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document.write( "                0.10x + 0.05(36-x) = 2.15\r\n" );
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document.write( "Multiply through by 100\r\n" );
document.write( "                 \r\n" );
document.write( "                      10x + 5(36-x) = 215\r\n" );
document.write( "                     10x + 180 - 5x = 215\r\n" );
document.write( "                           5x + 180 = 215\r\n" );
document.write( "                                 5x = 35\r\n" );
document.write( "                                  x = \r\n" );
document.write( "                                  x = 7\r\n" );
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document.write( "So there are 7 dimes and 36-7 or 29 nickels.     \r\n" );
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document.write( "Edwin

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