document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=171665>Question 171665</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0395585309/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Jo has37 coins(all nickels, dimes, andquarters) worth $5.50. She has 4 more quarters than nickels. How many dimes does she have? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #126854 by </B><A HREF=/tutors/aboutme.mpl?userid=ptaylor><B>ptaylor(2198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ptaylor><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=ptaylor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=126854\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x=number of nickels<BR>\n" );
document.write( "Then x+4=number of quarters<BR>\n" );
document.write( "So the number of dimes would be:<BR>\n" );
document.write( "37-x-(x+4)=<BR>\n" );
document.write( "37-2x-4=<BR>\n" );
document.write( "33-2x----number of dimes\r<BR>\n" );
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document.write( "Now we are told that:<BR>\n" );
document.write( "(lets deal in pennies)<BR>\n" );
document.write( "5x+25(x+4)+10(33-2x)=550  get rid of parens (distributive)<BR>\n" );
document.write( "5x+25x+100+330-20x=550 collect like terms<BR>\n" );
document.write( "10x+430=550  subtract 430 from each side<BR>\n" );
document.write( "10x+430-430=550-430=<BR>\n" );
document.write( "10x=120  divide each side by 10<BR>\n" );
document.write( "x=12-----------------number of nickels<BR>\n" );
document.write( "x+4=12+4=16-------------number of quarters<BR>\n" );
document.write( "33-2x=33-24=9---------------number of dimes\r<BR>\n" );
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document.write( "CK<BR>\n" );
document.write( "5*12+25*16+9*10=550<BR>\n" );
document.write( "60+400+90=550<BR>\n" );
document.write( "550=550<BR>\n" );
document.write( "We could also solve this problem using three unknowns:<BR>\n" );
document.write( "x=number of nickels<BR>\n" );
document.write( "y=number of dimes<BR>\n" );
document.write( "z=number of quarters<BR>\n" );
document.write( "x+y+z=37-----------------------eq1<BR>\n" );
document.write( "5x+10y+25z=550------------------eq2<BR>\n" );
document.write( "z=x+4----------------------------eq3<BR>\n" );
document.write( "Substitute z=x+4 into eq1 and eq2:<BR>\n" );
document.write( "2x+y=33-------------eq1a<BR>\n" );
document.write( "30x+10y=450-----------eq2a<BR>\n" );
document.write( "Multiply eq1a by 15 and subtract eq2a from it:<BR>\n" );
document.write( "5y=45<BR>\n" );
document.write( "y=9---------------number of dimes\r<BR>\n" );
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document.write( "Hope this helps---ptaylor </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );