document.write( "Question 1129508: Teresa has some dimes and quarters. If she has 28 coins worth a total of
\n" ); document.write( "$4.90, how many of each type of coin does she have? \n" ); document.write( "

Algebra.Com's Answer #746092 by ikleyn(52832) $\"\"$ $\"About$

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document.write( "Let D be the number of dimes, and let Q be the number of quarters.\r\n" );
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document.write( "Then you have this system of 2 equations in 2 unknowns\r\n" );
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document.write( "   D +    Q = 28             (1)    (there are 28 coins, in all)\r\n" );
document.write( "10*D + 25*Q = 490   cents    (2)    (the total)\r\n" );
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document.write( "You can solve the system by different methods.\r\n" );
document.write( "Let me call some of them: Substitution; Elimination; Cramer's rule (using determinants).\r\n" );
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document.write( "What you choose, depends on your level in Math and on your preferences.\r\n" );
document.write( "I don't know what your level and preferences are.\r\n" );
document.write( "So I will choose the most simple - Substitution.\r\n" );
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document.write( "From eq(1) express  D = 28-Q and substitute it into eq(2), replacing D there. You will get\r\n" );
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document.write( "10*(28-Q) + 25*Q = 490\r\n" );
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document.write( "280 - 10Q + 25Q = 490\r\n" );
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document.write( "15Q = 490 - 280 = 210\r\n" );
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document.write( "Q =  = 14.\r\n" );
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document.write( "Answer.  14 quarters and (the rest) 28-14 = 14 dimes.\r\n" );
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\n" ); document.write( "\n" ); document.write( "There are different methods for solving such problems:
\n" ); document.write( "    - using system of two equations (as in this post);
\n" ); document.write( "    - using single equation in one single unknown;
\n" ); document.write( "    - and simple logical methods without using equations.\r
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\n" ); document.write( "\n" ); document.write( "You may learn this subject and different methods from the lesson\r
\n" ); document.write( "\n" ); document.write( "    - Three methods for solving standard (typical) coin word problems\r
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\n" ); document.write( "\n" ); document.write( "For coin problems and their detailed solutions see the lessons in this site:\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( "    - Non-typical coin problems \r
\n" ); document.write( "\n" ); document.write( "    - Santa Claus helps solving coin problem\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 attentively and become an expert in this field.\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( "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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