document.write( "Question 1051922: A coin bank contains only nickels and dimes. The total value of the coins in the bank is $2.45. If the nickels were dimes and the dimes were nickels, the total value of the coins would be $2.80. Find the number of nickels in the bank.
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Algebra.Com's Answer #667369 by ikleyn(52788) $\"\"$ $\"About$

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\n" ); document.write( "A coin bank contains only nickels and dimes. The total value of the coins in the bank is $2.45.
\n" ); document.write( "If the nickels were dimes and the dimes were nickels, the total value of the coins would be $2.80.
\n" ); document.write( "Find the number of nickels in the bank.
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document.write( "Let n be the number of nickels and d be the number of dimes.\r\n" );
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document.write( "Then \r\n" );
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document.write( "5n + 10d = 245 cents   (1)    (\"The total value of the coins in the bank is $2.45. \")\r\n" );
document.write( "10n + 5d = 280 cents   (2)    (\"If the nickels were dimes and the dimes were nickels, the total value of the coins would be $2.50\")\r\n" );
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document.write( "Cancel the factor 5 in both sides of both equations. You will get\r\n" );
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document.write( "n + 2d = 49            (3)\r\n" );
document.write( "2n + d = 56            (4)\r\n" );
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document.write( "From (3), express n = 49-2d and substitute it into (4). You will get\r\n" );
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document.write( "2*(49-2d) + d = 56.\r\n" );
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document.write( "Simplify and solve for d:\r\n" );
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document.write( "98 - 4d + d = 56,  or\r\n" );
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document.write( "-3d = 56 - 98  --->  -3d = -42  --->  d = 14.\r\n" );
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document.write( "Thus the number of dimes is 14.\r\n" );
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document.write( "Then the number of nickels, from (3), is n = 49-2d = 49 - 2*14 = 21.\r\n" );
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document.write( "Check it on your own.\r\n" );
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document.write( "Answer.  14 dimes and 21 nickels.\r\n" );
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\n" ); document.write( "\n" ); document.write( "There is entire bunch of the 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( "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( "It contains many other solved word problems, as well as many other interesting and useful things.\r
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