document.write( "Question 1114360: You have 23 coins, including nickels, dimes, and quarters. If you have two more dimes than quarters, and the total value of the coins is $2.50. How many of each kind of coin do you have?\r
\n" ); document.write( "\n" ); document.write( "Define the variables you will be using to solve this problem.
\n" ); document.write( "Set up the problem by using algebraic equations to represent the problem.
\n" ); document.write( "Put the equations in matrix form.\r
\n" ); document.write( "\n" ); document.write( "q+d+n=23\r
\n" ); document.write( "\n" ); document.write( "D=q+2
\n" ); document.write( "0.25q+0.10d+0.05n=$2.50
\n" ); document.write( "0.25q+0.10(q+2)+0.05n=2.50
\n" ); document.write( "25q+10q+5n=250
\n" ); document.write( "35q+5n=250
\n" ); document.write( "I am so confused with this problem, I started to set it up and blanked. Am I even close to the algebraic equation?
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Algebra.Com's Answer #729313 by ikleyn(52814) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "Your first equation is\r\n" );
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document.write( "Q + D + N = 23\r\n" );
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document.write( "Your second equation is \r\n" );
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document.write( "D = Q + 2.\r\n" );
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document.write( "From these two equations you have\r\n" );
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document.write( "Q + (Q+2) + N = 23  \r\n" );
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document.write( "2Q + N = 21.       (1)\r\n" );
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document.write( "Now the money equation is\r\n" );
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document.write( "25Q + 10D + 5N = 250   cents,   or\r\n" );
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document.write( "25Q + 10*(Q+2) + 5N = 250,   or, equivalently\r\n" );
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document.write( "35Q + 5N = 230.    (2)\r\n" );
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document.write( "Thus you have this system of two equations in two unknowns\r\n" );
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document.write( " 2Q +  N = 21,     (1)\r\n" );
document.write( "35Q + 5N = 230     (2)\r\n" );
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document.write( "Divide eq(2) by 5 (both sides).  Keep eq(1) as is.\r\n" );
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document.write( " 2Q + N = 21       (1')\r\n" );
document.write( " 7Q + N = 46       (2')\r\n" );
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document.write( "Now subtract eq(1') from eq(2')\r\n" );
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document.write( " 5Q = 46 - 21 = 25  ====>  Q =  = 5.\r\n" );
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document.write( "5 quarters.  From (1')  N = 21 - 2Q = 21 - 2*5 = 11.\r\n" );
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document.write( "11 nickels.  Dimes = Q+2 = 5+2 = 7.\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( "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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