document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1158500>Question 1158500</A>: <I><SPAN STYLE=\"word-break: break-all;\"> this is the question: “How can I have $23.50 in change consisting of dimes, quarters, halves, and dollars with one third as many halves as dimes, twice as many quarters as dimes and 7 more dollars than halves” </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #781452 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13203)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=781452\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "No!  DON'T use 4 variables and write and solve a system of 4 equations...!<br><BR>\n" );
document.write( "Take the time to analyze the given information and try to write a single equation.<br><BR>\n" );
document.write( "The first piece of information is \"one-third as many halves as dimes\".  We could let our variable x be the number of dimes; but then the number of halves would be (1/3)x.  Fractions always make calculations more complicated; so let's start with our variable x as the number of halves.  So<br><BR>\n" );
document.write( "let x = # of half dollars<BR>\n" );
document.write( "then 3x = # of dimes  [\"one third as many halves as dimes\"]<BR>\n" );
document.write( "then 6x = # of quarters  [\"twice as many quarters as dimes\"]<BR>\n" );
document.write( "then x+7 = # of dollars  [\"7 more dollars than halves\"]<br><BR>\n" );
document.write( "Now we have a single equation in one variable to solve -- far less work than solving a system of 4 equations and 4 unknowns.<br><BR>\n" );
document.write( "Writing the equation in cents (again to avoid the difficulty of working with decimals):<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=50%28x%29%2B10%283x%29%2B25%286x%29%2B100%28x%2B7%29+=+2350 ALIGN=MIDDLE  ALT=\"50%28x%29%2B10%283x%29%2B25%286x%29%2B100%28x%2B7%29+=+2350\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=50x%2B30x%2B150x%2B100x%2B700+=+2350 ALIGN=MIDDLE  ALT=\"50x%2B30x%2B150x%2B100x%2B700+=+2350\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=330x+=+1650 ALIGN=MIDDLE  ALT=\"330x+=+1650\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+1650%2F330+=+5 ALIGN=MIDDLE  ALT=\"x+=+1650%2F330+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER:<BR>\n" );
document.write( "dollars: x+7 = 12<BR>\n" );
document.write( "halves: x = 5<BR>\n" );
document.write( "quarters: 6x = 30<BR>\n" );
document.write( "dimes: 3x = 15<br><BR>\n" );
document.write( "CHECK: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%28100%29%2B5%2850%29%2B30%2825%29%2B15%2810%29+=+1200%2B250%2B750%2B150+=+2350 ALIGN=MIDDLE  ALT=\"12%28100%29%2B5%2850%29%2B30%2825%29%2B15%2810%29+=+1200%2B250%2B750%2B150+=+2350\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );