document.write( "Question 1113748: A box contains $7.15 in nickels, dimes, and quarters. There are 41 coins in all, and the sum of the numbers of nickels and dimes is 3 less than the number of quarters. How many coins of each kind are there? \n" ); document.write( "

Algebra.Com's Answer #728833 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "(1)  nickels + dimes + quarters = 41      ( <<<---=== given )\r\n" );
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document.write( "     N       + D     + Q        = 41      ( the same )\r\n" );
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document.write( "(2)  N       + D   = Q - 3                ( <<<---=== given )\r\n" );
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document.write( "========>  Q + (Q-3) = 41\r\n" );
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document.write( "          2Q - 3 = 41  ====>  2Q = 41 + 3 = 44  ====>  Q = 22\r\n" );
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document.write( "So, we found number of quarters.  It is 22.\r\n" );
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document.write( "Next, you can reduce the problem from 3 unknowns to only two of them:\r\n" );
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document.write( "    we have 41-22 = 19 nickels and dimes, that are worth  7.15 - 22*0.25 = 1.65 dollars.\r\n" );
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document.write( " N +   D =  19      (coins)    (1)\r\n" );
document.write( "5N + 10D = 165      (cents)    (2)\r\n" );
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document.write( "Simplify\r\n" );
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document.write( " N +   D =  19                 (1')\r\n" );
document.write( " N +  2D =  33                 (2')\r\n" );
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document.write( "Subtract eq(1') from eq(2').\r\n" );
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document.write( "      D = 33-19 = 14.\r\n" );
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document.write( "Answer.  14 dimes,  22 quarters  and  19-14 = 5 nickels.\r\n" );
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document.write( "Check.   5*5 + 14*10 + 22*25 = 715 cents.   ! Correct !\r\n" );
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\n" ); document.write( "There is entire bunch of lessons on coin problems\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( "    - Three methods for solving standard (typical) coin word problems\r
\n" ); document.write( "\n" ); document.write( "    - More complicated coin problems\r
\n" ); document.write( "\n" ); document.write( "    - Solving coin problems mentally by grouping without using equations\r
\n" ); document.write( "\n" ); document.write( "    - Santa Claus helps solving coin problem\r
\n" ); document.write( "\n" ); document.write( "    - OVERVIEW of lessons on coin word problems\r
\n" ); document.write( "\n" ); document.write( "in this site.\r
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\n" ); document.write( "\n" ); document.write( "You will find there the lessons for all levels - from introductory to advanced,
\n" ); document.write( "and for all methods used - from one equation to two equations and even without equations. \r
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\n" ); document.write( "\n" ); document.write( "Read them and become an expert in solution of coin problems.\r
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\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-I in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this online textbook under the topic \"Coin problems\".\r
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\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Save the link to this online textbook together with its description\r
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\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-I
\n" ); document.write( "https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson\r
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\n" ); document.write( "\n" ); document.write( "to your archive and use it when it is needed.\r
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