document.write( "Question 1051865: A coin bank contains only nickels and dimes. The total value of the coins in the bank is $3.50. If the nickels were dimes and the dimes were nickels, the total value of the coins would be $2.50. Find the number of nickels in the bank. \n" ); document.write( "

Algebra.Com's Answer #667340 by ikleyn(52847) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "A coin bank contains only nickels and dimes. The total value of the coins in the bank is $3.50.
\n" ); document.write( "If the nickels were dimes and the dimes were nickels, the total value of the coins would be $2.50.
\n" ); document.write( "Find the number of nickels in the bank.
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "Let n be the number of nickels and d be the number of dimes.\r\n" );
document.write( "\r\n" );
document.write( "Then \r\n" );
document.write( "\r\n" );
document.write( "5n + 10d = 350 cents   (1)    (\"The total value of the coins in the bank is $3.50. \")\r\n" );
document.write( "10n + 5d = 250 cents   (2)    (\"If the nickels were dimes and the dimes were nickels, the total value of the coins would be $2.50\")\r\n" );
document.write( "\r\n" );
document.write( "Cancel the factor 5 in both sides of both equations. You will get\r\n" );
document.write( "\r\n" );
document.write( "n + 2d = 70            (3)\r\n" );
document.write( "2n + d = 50            (4)\r\n" );
document.write( "\r\n" );
document.write( "From (3), express n = 70-2d and substitute it into (4). You will get\r\n" );
document.write( "\r\n" );
document.write( "2*(70-2d) + d = 50.\r\n" );
document.write( "\r\n" );
document.write( "Simplify and solve for d:\r\n" );
document.write( "\r\n" );
document.write( "140 - 4d + d = 50,  or\r\n" );
document.write( "\r\n" );
document.write( "-3d = 50 - 140  --->  -3d = -90  --->  d = 30.\r\n" );
document.write( "\r\n" );
document.write( "Thus the number of dimes is 30.\r\n" );
document.write( "\r\n" );
document.write( "Then the number of nickels, from (3), is n = 70-2d = 70 - 2*30 = 10.\r\n" );
document.write( "\r\n" );
document.write( "Check it on your own.\r\n" );
document.write( "\r\n" );
document.write( "Answer.  30 dimes and 10 nickels.\r\n" );
document.write( "

\r
\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
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Read them and become an expert in solution of coin problems.\r
\n" ); document.write( "
\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
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "It contains many other solved word problems, as well as many other interesting and useful things.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );