document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=231061>Question 231061</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A cashier goes to the bank to get $10 worth of change. He requests twice as many<BR>\n" );
document.write( "quarters as half dollars, twice as many dimes as quarters, three times as many<BR>\n" );
document.write( "nickels as dimes, and no pennies or dollars. How many of each coin did the cashier<BR>\n" );
document.write( "get? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #171080 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=171080\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> f = number of dollars<BR>\n" );
document.write( "h = number of half dollars<BR>\n" );
document.write( "q = number of quarters<BR>\n" );
document.write( "d = number of dimes<BR>\n" );
document.write( "n = number of nickels<BR>\n" );
document.write( "p = number of pennies.\r<BR>\n" );
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document.write( "total money equals $10.00\r<BR>\n" );
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document.write( "f * 1 = amount of money in dollars<BR>\n" );
document.write( "h * .5 = amount of money in half dollars<BR>\n" );
document.write( "q * .25 = amount of money in quarters<BR>\n" );
document.write( "d * .1 = amount of money in dimes<BR>\n" );
document.write( "n * .05 = amount of money in nickels<BR>\n" );
document.write( "p * .01 = amount of money in pennies\r<BR>\n" );
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document.write( "Total money collected equals $10.00\r<BR>\n" );
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document.write( "1*f + .5*h + .25*q + .10*d + .05*n + .01*p = 10\r<BR>\n" );
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document.write( "f and p are equal to 0, so this equation becomes:\r<BR>\n" );
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document.write( "1*0 + .5*h + .25*q + .10*d + .05*n + .01*0 = 10\r<BR>\n" );
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document.write( "Simplify this equation to get:\r<BR>\n" );
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document.write( ".5*h + .25*q + .10*d + .05*n = 10\r<BR>\n" );
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document.write( "Since:\r<BR>\n" );
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document.write( "q = 2*h (number of quarters equals 2 times the number of half dollars)<BR>\n" );
document.write( "d = 2*q (number of dimes equals 2 times the number of quarters)<BR>\n" );
document.write( "n = 3*d (number of nickels equals 3 times the number of dimes)\r<BR>\n" );
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document.write( "Replace n with 3*d to get:\r<BR>\n" );
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document.write( ".5*h + .25*q + .10*d + .05*3*d = 10\r<BR>\n" );
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document.write( "Replace d with 2*q to get:\r<BR>\n" );
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document.write( ".5*h + .25*q + .10*2*q + .05*3*2*q = 10\r<BR>\n" );
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document.write( "Replace q with 2*d to get:\r<BR>\n" );
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document.write( ".5*h + .25*2*h + .10*2*2*h + .05*3*2*2*h = 10\r<BR>\n" );
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document.write( "Simplify to get:\r<BR>\n" );
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document.write( ".5*h + .5*h + .4*h + .6*h = 10\r<BR>\n" );
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document.write( "Combine like terms to get:\r<BR>\n" );
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document.write( "2*h = 10\r<BR>\n" );
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document.write( "Divide both sides by 2 to get:\r<BR>\n" );
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document.write( "h = 5\r<BR>\n" );
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document.write( "Since q = 2*h, then q = 10<BR>\n" );
document.write( "Since d = 2*q, then d = 20<BR>\n" );
document.write( "Since n = 3*d, then n = 60\r<BR>\n" );
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document.write( "You have:\r<BR>\n" );
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document.write( "h = 5 * .5 = $2.50<BR>\n" );
document.write( "q = 10 * .25 = $2.50<BR>\n" );
document.write( "d = 20 * .1 = $1.00<BR>\n" );
document.write( "n = 60 * .05 = $3.00\r<BR>\n" );
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document.write( "Total = $10.00 which is correct.\r<BR>\n" );
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document.write( "Cashier gets:\r<BR>\n" );
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document.write( "5 half dollars<BR>\n" );
document.write( "10 quarters<BR>\n" );
document.write( "20 dimes<BR>\n" );
document.write( "60 nickels\r<BR>\n" );
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document.write( " </SPAN>\n" );
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