document.write( "Question 1105246: Steve has only nickels and quarters. If he has 5 more quarters than nickels and the total value of all the coins is $5.15, find the number of coins of each type. Define the variable(s), write an equation and solve. \n" ); document.write( "
Algebra.Com's Answer #720007 by ikleyn(53763)\"\" \"About 
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\n" ); document.write( "1.   Two equations approach\r
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document.write( " Q = N + 5             (1)     (counting coins: \"5 more quarters than nickels\")\r\n" );
document.write( "5N + 25Q = 515         (2)     (counting cents)\r\n" );
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document.write( "Next substitute (1) into eq(2). You will get\r\n" );
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document.write( "5N + 25*(N+5) = 515    (3)  ====>\r\n" );
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document.write( "5N + 25N + 125 = 515  ====>  30N = 515-125 = 390  ====>  N = \"390%2F30\" = 13.\r\n" );
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document.write( "Answer.  13 nickels and 13+5 = 18 quarters.\r\n" );
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document.write( "Check.   13*5 + 18*25 = 515 cents  ! Correct !\r\n" );
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\n" ); document.write( "\n" ); document.write( "2.   One equation approach\r
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document.write( "Let N be the number of nickels. Then the number of quarters is (N+5), according to the condition.\r\n" );
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document.write( "The \"money\" equation is\r\n" );
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document.write( "5N + 25*(N+5) = 515   cents    - exactly as the equation (3)  above.\r\n" );
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document.write( "The solution and the answer are the same as in the part 1.\r\n" );
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\n" ); document.write( "\n" ); document.write( "3.   Logical analysis without using equation/equations\r
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document.write( "For a minute, take away (mentally) 5 quarters from the collection.\r\n" );
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document.write( "Then you have equal number of nickels and quarters in the updated collection which is worth 515-5*25 = 390 cents now.\r\n" );
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document.write( "You can group the coins in the updated collection in the sets consisting of 1 nickel and one quarter each.\r\n" );
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document.write( "Each set is worth 25+5 = 30 cents and the number of sets is \"390%2F30\" = 13.\r\n" );
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document.write( "Then it is clear that the original collection counts 13 nickels and 13+5 = 18 quarters.\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.
\n" ); document.write( "Pay special attention to the lesson marked (*) in the list - it is the TWIN to this solution.\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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