document.write( "Question 460447: a piggy bank contains nickels, dimes, and quarters. The number of dimes is three more than the number of nickels and the number of quarters is four less than the number of nickels. If the value of the coins is less than $10, what is the maximum number of nickels in the bank? \n" ); document.write( "
Algebra.Com's Answer #315842 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "\r\n" );
document.write( ">>...The number of dimes is three more than the number of nickels...<<\r\n" );
document.write( "\r\n" );
document.write( "                       d = n + 3\r\n" );
document.write( "\r\n" );
document.write( ">>...the number of quarters is four less than the number of nickels...<<\r\n" );
document.write( "\r\n" );
document.write( "                       q = n - 4\r\n" );
document.write( "\r\n" );
document.write( ">>...the value of the coins is less than $10,...<< \r\n" );
document.write( "\r\n" );
document.write( "$0.05n + $0.10d + $0.25q < $10.00\r\n" );
document.write( "\r\n" );
document.write( "Multiply that by 100 and drop $ marka:\r\n" );
document.write( "\r\n" );
document.write( "          5n + 10d + 25q < 1000\r\n" );
document.write( "\r\n" );
document.write( "Divide through by 5\r\n" );
document.write( "\r\n" );
document.write( "             n + 2d + 5q < 200\r\n" );
document.write( "\r\n" );
document.write( "Substitute d = n + 3 and q = n - 4\r\n" );
document.write( "\r\n" );
document.write( " n + 2(n + 3) + 5(n - 4) < 200\r\n" );
document.write( "\r\n" );
document.write( "    n + 2n + 6 + 5n - 20 < 200\r\n" );
document.write( "\r\n" );
document.write( "                 8n - 14 < 200\r\n" );
document.write( "\r\n" );
document.write( "                      8n < 214\r\n" );
document.write( "                       \r\n" );
document.write( "                       n < 26.75\r\n" );
document.write( "\r\n" );
document.write( "        \r\n" );
document.write( "The answer is 26 nickels. for that is the largest whole number\r\n" );
document.write( "that does not exceed 26.75\r\n" );
document.write( "\r\n" );
document.write( "In fact the maximum number of dimes, the maximum number of\r\n" );
document.write( "nickels, and the maximum number of quarters are all three\r\n" );
document.write( "achieved if the piggy bank contains $9.70 with 29 dimes, \r\n" );
document.write( "26 nickels and 22 quarters.\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );