document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=858207>Question 858207</A>: <I><SPAN STYLE=\"word-break: break-all;\"> There are 35 coins in a jar. There are a combination of loonies and quarters. The Value of the coins is 17.75. How many loonies are there? This is how I attempted this.. however it does not make sense... as I know there has to be 12 loonies.... How would I do this using an equation?? \r<BR>\n" );
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document.write( "100L + 25(35-L) = 1775<BR>\n" );
document.write( "100L + 875 - 25l = 1775<BR>\n" );
document.write( "75l+875=1175<BR>\n" );
document.write( "75L + 300<BR>\n" );
document.write( "75L/75 + 300/75<BR>\n" );
document.write( "L=4<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #517110 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39618)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=517110\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This is not a linear system, at least not how I analyze it.  \r<BR>\n" );
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document.write( "Let Q = how many quarts<BR>\n" );
document.write( "let L = how many loonies<BR>\n" );
document.write( "let r = rate of dollars per coin for the loonies; we already know that for the quarters, that rate is 0.25.  We do not yet know this rate for loonies.\r<BR>\n" );
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document.write( "Coin Count:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%2BQ=35 ALIGN=MIDDLE  ALT=\"L%2BQ=35\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Dollars Count: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Lr%2B%28.025%29Q=17.75 ALIGN=MIDDLE  ALT=\"Lr%2B%28.025%29Q=17.75\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "No other equation was found possible.  We only know that Q, and L, must be Natural Numbers, and less clear about r, except it is greater than zero, and rational.  \r<BR>\n" );
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document.write( "Solving the system symbolically for r will give:<BR>\n" );
document.write( "...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28r=%2871-Q%29%2F%284%2835-Q%29%29%29 ALIGN=MIDDLE  ALT=\"highlight_green%28r=%2871-Q%29%2F%284%2835-Q%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So, this comes from a nonlinear system in three unknowns for two equations.  The only way I see to find any possible reasonably answer is the crudely test values of Q from 34 to 1; compute r for each value of Q.  We must have values of r such that r is rational, and r greater than 0.  A simple computer program might be the way to go, or maybe use the formula in a graphing calculator.\r<BR>\n" );
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document.write( "NOTE: You may find several possible answers for this.  I just checked a couple different values for r from the equation above just found.  If Q is 33, then you find r = 9 dollars per loony.  Other values for Q may also be useful.  The question as given seems to be open-ended. </SPAN>\n" );
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