document.write( "Question 1194373: Joe has a collection of nickels and dimes that is worth $8.30. If the number of dimes were doubled and the number of nickels were increased by 18, the value of the coins would be $14.50. How many dimes does he have? \n" ); document.write( "

Algebra.Com's Answer #826572 by ikleyn(53937) $\"\"$ $\"About$

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\n" ); document.write( "Joe has a collection of nickels and dimes that is worth $8.30.
\n" ); document.write( "If the number of dimes were doubled and the number of nickels were increased by 18,
\n" ); document.write( "the value of the coins would be $14.50. How many dimes does he have?
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\n" ); document.write( "\n" ); document.write( " Let solve it mentally, with easy steps.\r
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document.write( "We have two collections of coins: one real collection and the other \r\n" );
document.write( "imaginary collection.\r\n" );
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document.write( "Let construct another imaginary collection, which has the doubled number of dimes, \r\n" );
document.write( "but the same number of nickels as the real collection.\r\n" );
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document.write( "This another imaginary collection is worth $14.50 - 18*$0.05 = $14.50 - $0.90 = $13.60.\r\n" );
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document.write( "Comparing with the original (real) collection, it has the same number of nickels \r\n" );
document.write( "and doubled number of dimes.\r\n" );
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document.write( "Hence, the dimes in the original collections are worth the difference between \r\n" );
document.write( "$13.60 and $8.30, i.e. $5.30, or 530 cents.\r\n" );
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document.write( "From it, you conclude that the number of dimes in the original collection is  = 53.\r\n" );
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document.write( "                It is your ANSWER.\r\n" );
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document.write( "CHECK.  Then the number of nickels in real collection is   =  = 60\r\n" );
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document.write( "        and imaginary collection is worth  2*530 + (60+18)*5 = 1450 cents,  or $14.50.   ! Correct !\r\n" );
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