document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=105059>Question 105059</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A change machine contains nickels, dimes, and quarters. There are 75 coins in the machine, and the value of the coins is $7.25. There are 5 times as many nickels as dimes. Find the number of coins of each type in the machine. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #76513 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=76513\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> :<BR>\n" );
document.write( "A change machine contains nickels, dimes, and quarters.<BR>\n" );
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document.write( "Just write an equation for each statement:<BR>\n" );
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document.write( "\"There are 75 coins in the machine,\"<BR>\n" );
document.write( "n + d + q = 75<BR>\n" );
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document.write( "\"the value of the coins is $7.25.\"<BR>\n" );
document.write( ".05n + .10n + .25q = 7.25<BR>\n" );
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document.write( "\" There are 5 times as many nickels as dimes.\"<BR>\n" );
document.write( "n = 5d<BR>\n" );
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document.write( "Find the number of coins of each type in the machine.<BR>\n" );
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document.write( "Substitute 5d for n in the 1st equation:<BR>\n" );
document.write( "5d + d + q = 75<BR>\n" );
document.write( "6d + q = 75<BR>\n" );
document.write( "q = (75-6d); use this for substitution later<BR>\n" );
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document.write( "Substitute 5d for n in the 2nd equation:<BR>\n" );
document.write( ".05(5d) + .10d + .25q = 7.25<BR>\n" );
document.write( ".25d + .10d + .25q = 7.25<BR>\n" );
document.write( ".35d + .25q = 7.25<BR>\n" );
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document.write( "In the above equation substitute (75-6d) for q:<BR>\n" );
document.write( ".35d + .25(75-6d) = 7.25<BR>\n" );
document.write( ".35d + 18.75 - 1.5d = 7.25<BR>\n" );
document.write( ".35d - 1.5d = 7.25 - 18.75<BR>\n" );
document.write( "-1.15d = -11.5<BR>\n" );
document.write( "d = -11.5/-1.15<BR>\n" );
document.write( "d = +10 dimes<BR>\n" );
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document.write( "Find the nickels from n = 5d<BR>\n" );
document.write( "n = 5(10)<BR>\n" );
document.write( "n = 50 nickels<BR>\n" );
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document.write( "Find q using the 1st equation:<BR>\n" );
document.write( "50 + 10 + q = 75<BR>\n" );
document.write( "60 + q = 75<BR>\n" );
document.write( "q = 75 - 60<BR>\n" );
document.write( "q = 15 quarters<BR>\n" );
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document.write( "Check our solutions on the 2nd equation:.<BR>\n" );
document.write( ".05(50) + .10(10) + .25(15) = <BR>\n" );
document.write( "2.50 + 1.00 + 3.75 = 7.25; confirms our solutions<BR>\n" );
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document.write( "Did this makes sense to you? A lot of steps but each one is logical and simple.<BR>\n" );
document.write( "Any questions?  </SPAN>\n" );
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