document.write( "Question 1059667: Ana has a piggy bank that contains nickels, dimes, and quarters. When she opens the bank and counts her money, she has $3.35. She counted twice as many nickels as quarters, and two more dimes than quarters. How many dimes does she have? \n" ); document.write( "

Algebra.Com's Answer #674740 by ikleyn(52798) $\"\"$ $\"About$

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\n" ); document.write( "Ana has a piggy bank that contains nickels, dimes, and quarters. When she opens the bank and counts her money, she has $3.35.
\n" ); document.write( "She counted twice as many nickels as quarters, and two more dimes than quarters. How many dimes does she have?
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document.write( "Let \"x\" be the number of quarters in the collection.\r\n" );
document.write( "Then the number of nickels is 2x and the number of dimes is (x+2), according to the condition.\r\n" );
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document.write( "The nickel contribute   5*(2x)    cents to the total.\r\n" );
document.write( "The dimes contribute    10*(x+2)  cents to the total.\r\n" );
document.write( "the quarters contribute  25x      cents to the total.\r\n" );
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document.write( "The total is 5*(2x) + 10*(x+2) + 25x.\r\n" );
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document.write( "Hence, the \"value\" equation is\r\n" );
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document.write( "5*(2x) + 10*(x+2) + 25x = 335.\r\n" );
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document.write( "Simplify and solve for x:\r\n" );
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document.write( "10x + 10x + 20 + 25x = 335,\r\n" );
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document.write( "45x = 335 - 20,\r\n" );
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document.write( "45x = 315  --->  x =  = 7.\r\n" );
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document.write( "Answer.  7 quarters, 2*7 = 14 nickels, 7 + 2 = 9 dimes.\r\n" );
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document.write( "Check.   7*25 + 14*5 + 9*10 = 335 cents. Correct.\r\n" );
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\n" ); document.write( "\n" ); document.write( "The lesson to learn from this solution:\r
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\n" ); document.write( "\n" ); document.write( "1. First choose the major unknown reasonably.\r
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\n" ); document.write( "\n" ); document.write( "2. Second, express other unknowns via the major unknown.\r
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\n" ); document.write( "\n" ); document.write( "3. Then make an equation.\r
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\n" ); document.write( "\n" ); document.write( "4. Then solve the equation.\r
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\n" ); document.write( "\n" ); document.write( "It is your algorithm.\r
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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( "    - 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( "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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