document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=135084>Question 135084</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The Jaspers collect nickels, dimes, and quarters in a jar. When they count the change in the jar, there are twice as many nickels as there are quarters. If there is $15.30 in dimes and $74.80 in all, how many quarters are there? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #98930 by </B><A HREF=/tutors/aboutme.mpl?userid=algebrapro18><B>algebrapro18(249)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=algebrapro18><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=98930\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The Jaspers collect nickels, dimes, and quarters in a jar. When they count the change in the jar, there are twice as many nickels as there are quarters. If there is $15.30 in dimes and $74.80 in all, how many quarters are there?\r<BR>\n" );
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document.write( "well let n = number of nickels, d be the number of dimes, and q be the number of quarters.  Now we need to set up a system of three equations with three unknowns.  We know that the total monetary amount in dimes is 15.30 so we get the equation .10d = 15.30 as one of our equations.  We also know that there are twice as many nickels as there are quarters.  So the equation for this would be 2n = q.  we also now that there if you add up all the change in the jar there is $74.80  In a mathematical equation this becomes .1d + .05n + .25q = 75.80.  So now we have our three equations with three unknowns. \r<BR>\n" );
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document.write( ".1d + .05n + .25q = 75.80.<BR>\n" );
document.write( "2n = q<BR>\n" );
document.write( ".10d = 15.30\r<BR>\n" );
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document.write( "Now we go about doing the algebra to find how many quarters there are.\r<BR>\n" );
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document.write( "solving the third equation we can find out how many dimes there are and we can use this to find how many quarters there are.\r<BR>\n" );
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document.write( ".10d = 15.30<BR>\n" );
document.write( "d = 153\r<BR>\n" );
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document.write( "now we know that there were 153 dimes in that jar.  We can use this to rewrite the system and now its a system of two equations with 2 unknowns.\r<BR>\n" );
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document.write( ".1(153) + .05n + .25q = 75.80.<BR>\n" );
document.write( "2n = q\r<BR>\n" );
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document.write( "or simplifying you get\r<BR>\n" );
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document.write( ".05n + .25q = 60.50<BR>\n" );
document.write( "2n = q\r<BR>\n" );
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document.write( "now since you only want to know how many quarters there are you can solve the second equation for n and then plug that into the first equation and solve for q.\r<BR>\n" );
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document.write( "2n=q<BR>\n" );
document.write( "n = .5q\r<BR>\n" );
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document.write( ".05(.5q) + .25q = 60.50<BR>\n" );
document.write( ".025q + .25q = 60.50<BR>\n" );
document.write( ".275q = 60.50<BR>\n" );
document.write( "q = 220\r<BR>\n" );
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document.write( "so we know that there are 220 quarters in the jar. </SPAN>\n" );
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