document.write( "Question 489632: Please help me. I'm struggling with these word problems. This is too difficult. Diane has $1.65 in dimes and nickels. She has a total of 21 coins. How many of each does she have? \r
\n" ); document.write( "\n" ); document.write( "Suppose Tom has 14 coins totaling $2.30. If he has on dimes and quarters, how many of each does he have? \r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
Algebra.Com's Answer #333712 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "Start with the easy sentence first:\r\n" );
document.write( "

\n" ); document.write( "\"She has a total of 21 coins.\"
\n" ); document.write( "
\r\n" );
document.write( "Let d = the number of dime coins and n = the number of nickel coins.\r\n" );
document.write( "Then if you add them together you put a + sign between them like this\r\n" );
document.write( "\r\n" );
document.write( "d+n\r\n" );
document.write( "\r\n" );
document.write( "and since the total number of coins is 21, we have the equation\r\n" );
document.write( "\r\n" );
document.write( "d+n = 21\r\n" );
document.write( "\r\n" );
document.write( "Now look at the other clause:\r\n" );
document.write( "

\n" ); document.write( "\"...$1.65 in dimes and nickels.\"
\n" ); document.write( "
\r\n" );
document.write( "If you multiply the number of dimes, d, by 10 cents you get 10d cents\r\n" );
document.write( "If you multiply the number of nickels, n, by 5 cents you get 5n cents\r\n" );
document.write( "If you add 10d cents and 6n cents, you put a + sign between them, like\r\n" );
document.write( "this:\r\n" );
document.write( "\r\n" );
document.write( "10d+5n\r\n" );
document.write( "\r\n" );
document.write( "That expression must represent the total number of cents. \r\n" );
document.write( "But you also know that the total number of cents in $1.65 is 165 cents.\r\n" );
document.write( "So 10d+5n must equal to 165.  So you have the equation\r\n" );
document.write( "\r\n" );
document.write( "    10d+5n = 165\r\n" );
document.write( "\r\n" );
document.write( "So you have the systme of equations\r\n" );
document.write( "\r\n" );
document.write( "d+n = 21\r\n" );
document.write( "10d+5n = 165\r\n" );
document.write( "\r\n" );
document.write( "which you can solve by substitution or elimination and get d=12, n=9\r\n" );
document.write( "\r\n" );
document.write( "If you don't know how to solve that system of equations, then\r\n" );
document.write( "post again asking how.\r\n" );
document.write( "\r\n" );
document.write( "----------------------\r\n" );
document.write( "

\n" ); document.write( "Suppose Tom has 14 coins totaling $2.30. If he has only dimes and quarters,
\n" ); document.write( "how many of each does he have?
\n" ); document.write( "
\r\n" );
document.write( "The exact same way. You'll get d=8, q=6\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );