document.write( "Question 1152796: Shelby has some nickels and quarters worth $2.30. Andrew has twice as many nickels as Shelby, but 3 less quarters that Shelby. Andrew's coins are worth $1.85. How many nickels and quarters does Shelby have? Any help is appreciated! \n" ); document.write( "

Algebra.Com's Answer #774881 by ikleyn(52778) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "

\r\n" );
document.write( "\r\n" );
document.write( "Let N and Q are the numbers of nickels and quarters that Shelby has (the values under the question).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Then Andrew has 2N nickels and (Q-3) quarters.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "You have these 2 equations for 2 unknowns\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    10N     + 25Q      = 230  cents   (1)    (Shelby's money)\r\n" );
document.write( "\r\n" );
document.write( "    10*(2N) + 25*(Q-3) = 185 cents    (2)    (Andrew's money)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Simplify and reduce to the standard form\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    10N + 25Q = 230     (3)\r\n" );
document.write( "\r\n" );
document.write( "    20N + 25Q = 260     (4)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "From equation (4), subtract equation (3)  (both sides)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     10N      = 30\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Hence,  N = 3.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Then from equation (1),  \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    10*3 + 25Q = 230,\r\n" );
document.write( "\r\n" );
document.write( "    25Q = 230 - 30 = 200\r\n" );
document.write( "\r\n" );
document.write( "      Q            = 200/25 = 8.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "ANSWER.  Shelby has  3 nickels and 8 quarters.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "You may check that my answer satisfies all conditions of the problem.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Do it on your own (!)\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );