document.write( "Question 1120064: Joey has 24 coins in his pocket. The coins are all nickels and dimes. The total value of the coins is $1.85. How many dimes does Joey have? \n" ); document.write( "

Algebra.Com's Answer #735720 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "     = 13 dimes.\r\n" );
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document.write( "    The rest 24 - 13 = 11 are nickels.\r\n" );
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document.write( "    Check.  11*5 + 13*10 = 185 cents.   ! Correct !\r\n" );
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document.write( "    Answer.  13 dimes, 11 nickels.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Explanation to the solution\r
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document.write( "Let assume that all 24 coins are nickels.  Then their total value would be 5*24 = 120 cents.\r\n" );
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document.write( "But the real value is 185, and the difference is  1805- 120 = 65 cents.   \r\n" );
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document.write( "    Notice, this difference is the NUMERATOR in my one-line solution.\r\n" );
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document.write( "Surely, you understand that the cause of this difference lies in the fact that we counted some dimes as nickels.\r\n" );
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document.write( "Now let's replace nickels by dimes. At each replacement, we decrease the difference in 5 cents,\r\n" );
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document.write( "so the total number of replacements is  the ratio   = 5 cents.\r\n" );
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document.write( "     Notice, this difference  10-5 = 5 cents is the DENOMINATOR  in my one-line solution.\r\n" );
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document.write( "Thus the ratio   =  = 13  is exactly the number of dimes in the collection.\r\n" );
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document.write( "This completes the explanation.\r\n" );
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\n" ); document.write( "\n" ); document.write( "So, you are explained how to solve the problem in one line.\r
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\n" ); document.write( "\n" ); document.write( "Also, you just learned this LOGICAL method on how to solve it.\r
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\n" ); document.write( "\n" ); document.write( "In the future, you can use EITHER of these two methods.
\n" ); document.write( "They both are classic methods for solving this type of coin problems.\r
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