document.write( "Question 1170563: Kiran reaches into her pocket and finds 28 coins with a total value of $4.10. The coins are nickels, dimes or quarters only. There are twice as many quarters as dimes. How many of each type of coin does Kiran have? \n" ); document.write( "

Algebra.Com's Answer #795415 by ikleyn(52942) $\"\"$ $\"About$

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\n" ); document.write( "Kiran reaches into her pocket and finds 28 coins with a total value of $4.10.
\n" ); document.write( "The coins are nickels, dimes or quarters only.
\n" ); document.write( "There are twice as many quarters as dimes. How many of each type of coin does Kiran have?
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document.write( "Let x be the number of dimes.\r\n" );
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document.write( "Then the number of quarters is  2x, according to the condition;\r\n" );
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document.write( "and the number of nickels is (28-x-2x) = (28-3x): they are the rest of coins.\r\n" );
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document.write( "Now you write the total money equation\r\n" );
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document.write( "    10x + 25*(2x) + 5*(28-3x) = 410   cents.\r\n" );
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document.write( "Simplify it step by step\r\n" );
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document.write( "    10x + 50x + 140 - 15x = 410\r\n" );
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document.write( "    10x + 50x - 15x       = 410 - 140\r\n" );
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document.write( "          45x             = 270\r\n" );
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document.write( "            x             = 270/45 = 6.\r\n" );
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document.write( "ANSWER.  6 dimes, 2*6 = 12 quarters and the rest coins,  28-6-12 = 10  are nickels.\r\n" );
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document.write( "CHECK.   Total money is  6*10 + 12*25 + 10*5 = 410  cents.   ! Correct !\r\n" );
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\n" ); document.write( "\n" ); document.write( "The remarkable fact is that the problem is solved using only one equation in one unknown.\r
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\n" ); document.write( "\n" ); document.write( "Using this approach has that advantages that the problem becomes accessible for 5th grade and 6th grade students
\n" ); document.write( "who are not familiar yet with systems of equations;\r
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\n" ); document.write( "\n" ); document.write( "it really teaches young students to THINK working on setup, and it provides the solution as simple as it should be.\r
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\n" ); document.write( "\n" ); document.write( "I am 129% convinced that the real purpose and real destination of this and other similar problems is to teach young students
\n" ); document.write( "to solve problems in the most simple way.\r
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\n" ); document.write( "\n" ); document.write( "To see many other similar solved problems (your TEMPLATES), look into the lesson\r
\n" ); document.write( "\n" ); document.write( " - Advanced coin problems \r
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