document.write( "Question 1042758: In a collection of dimes and quarters, the number of dimes is eight less than twice the number of quarters. The value of the collection is $8.20. Find the number of dimes and quarters. \n" ); document.write( "

Algebra.Com's Answer #657793 by ikleyn(52814) $\"\"$ $\"About$

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\n" ); document.write( "In a collection of dimes and quarters, the number of dimes is eight less than twice the number of quarters.
\n" ); document.write( "The value of the collection is $8.20. Find the number of dimes and quarters.
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\n" ); document.write( "\n" ); document.write( "Let me solve it mentally, without using equations.\r
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document.write( "Add 8 dimes to the collection (mentally).\r\n" );
document.write( "Then the total would be $ 8.20 + $0.80 = $9.00.\r\n" );
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document.write( "Then $9.00 consists of some number of dimes (d) and twice the number of quarters.\r\n" );
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document.write( "So, we have 3d coins, which we can re-group into d groups consisting of two quarters and one dime each.\r\n" );
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document.write( "d groups of coins worth 2*50+10 = 60 cents each group.\r\n" );
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document.write( "Obviously, the number of groups is  = 15.\r\n" );
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document.write( "Hence, originally we had 2*15 = 30 quarters and 15-8 = 7 dimes.\r\n" );
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document.write( "Check. 30*25 + 70 = 750 + 70 = 820 cents.\r\n" );
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document.write( "Answer.  30 quarters and 7 dimes.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "For coin problems, see the lessons\r
\n" ); document.write( "\n" ); document.write( "    - Coin problems\r
\n" ); document.write( "\n" ); document.write( "    - More Coin problems\r
\n" ); document.write( "\n" ); document.write( "    - Solving coin problems without using equations\r
\n" ); document.write( "\n" ); document.write( "    - Kevin and Randy Muise have a jar containing coins\r
\n" ); document.write( "\n" ); document.write( "    - Typical coin problems from the archive\r
\n" ); document.write( "\n" ); document.write( "in this site.\r
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