document.write( "Question 1109170: If you have 10 dimes and nickels in your pocket that total to $0.70, how many separate dimes and how many separate nickels do you have. \n" ); document.write( "
Algebra.Com's Answer #724172 by ikleyn(52879)\"\" \"About 
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\n" ); document.write( "\n" ); document.write( "        There are different methods to solve the problem.
\n" ); document.write( "        I will show you 3 (three) basic methods in this post.\r
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\n" ); document.write( "\n" ); document.write( "1- Algebra solution,   2 equations approach\r
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document.write( "Let d be the number of dimes and n be the number of nickels.\r\n" );
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document.write( "Then you have this system of two equations\r\n" );
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document.write( "  d +   n =  10,        (1)    (counting dimes)\r\n" );
document.write( "10d +  5n =  70.        (2)    (counting cents)\r\n" );
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document.write( "To solve it, multiply eq(1) by 5. You will have\r\n" );
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document.write( " 5d +  5n =  50,        (1')\r\n" );
document.write( "10d +  5n =  70.        (2')\r\n" );
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document.write( "Next subtract (1') from (2'). You will get\r\n" );
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document.write( "10d - 5d = 70 - 50,\r\n" );
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document.write( " 5d = 20  ====>  d = \"20%2F5\" = 4.\r\n" );
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document.write( "There are 4 dimes and 10-4 = 6 nickels.\r\n" );
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document.write( "Check.   4*10 + 6*5 = 70.    !  Correct !\r\n" );
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document.write( "Answer.  There are 4 dimes and 10-4 = 6 nickels.\r\n" );
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\n" ); document.write( "\n" ); document.write( "2- Algebra solution,   1 equation approach\r
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document.write( "Let  d be the number of dimes.\r\n" );
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document.write( "Then the number of nickels is (10-d). \r\n" );
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document.write( "The nickels contribute 5*(10-d) cents toward the total.\r\n" );
document.write( "The dimes   contribute 10*d     cents toward the total.\r\n" );
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document.write( "The total is  5*(10-d) + 10*d   cents.\r\n" );
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document.write( "From the other side, it is 70 cents, according to the condition.\r\n" );
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document.write( "It gives you an equation\r\n" );
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document.write( "5*(10-d) + 10*d = 70.     \r\n" );
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document.write( "Simplify and solve for n:\r\n" );
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document.write( "50 - 5d + 10d = 70 \r\n" );
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document.write( "5d = 70 - 50  \r\n" );
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document.write( "5d = 20  ====>  d = \"20%2F5\" = 4.\r\n" );
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document.write( "There are 4 dimes and 10-4 = 6 nickels.\r\n" );
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document.write( "You got the same answer.\r\n" );
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\n" ); document.write( "\n" ); document.write( "2- Logical analysis (MENTAL solution without using equations)\r
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document.write( "Imagine for a minute that all coins in the parking meter are NICKELS.\r\n" );
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document.write( "Then you would have 10*5 = 50 cents in the parking meter.\r\n" );
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document.write( "But in reality the money amount there is 70 cents, which is 70- 50 = 20 cents more than 50 cents.\r\n" );
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document.write( "Why we have this difference ?  - But of course, because we counted 10-cent dimes as 5-cent coins.\r\n" );
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document.write( "Then it is clear, that the number of dimes is  \"20%2F%2810-5%29\" = \"20%2F5\" = 4.\r\n" );
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document.write( "And you get the same answer.\r\n" );
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\n" ); document.write( "Congratulations !   You are now familiar with 3 basic methods for solving typical coin problems.\r
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\n" ); document.write( "\n" ); document.write( "I suggest that algebraic methods will be your basic methods for such problems,\r
\n" ); document.write( "\n" ); document.write( "and the logical analysis method will allow you to solve the problems MENTALLY without using equations.\r
\n" ); document.write( "\n" ); document.write( "I will be happy if it will make your horizon wider.\r
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\n" ); document.write( "To see other similar solved coin problems, look in the lessons\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( "    - Typical coin problems from the archive\r
\n" ); document.write( "\n" ); document.write( "    - Solving coin problems mentally by grouping without using equations\r
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\n" ); document.write( "\n" ); document.write( "To see how the logical method works for other similar problems, look into the lessons\r
\n" ); document.write( "\n" ); document.write( "    - Problem on two-wheel and three-wheel bicycles\r
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