document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=286376>Question 286376</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A woman has $2.15 in change in her purse, comprised entirely of dimes and quarters. Given that there are more quarters than dimes in her purse, what is the total number of coins?\r<BR>\n" );
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document.write( "A. 9 B. 10 C. 11 D. 12 E. 13 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #207674 by </B><A HREF=/tutors/aboutme.mpl?userid=ptaylor><B>ptaylor(2198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ptaylor><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=ptaylor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=207674\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x=number of quarters<BR>\n" );
document.write( "And y=number of dimes<BR>\n" );
document.write( "We are told that:<BR>\n" );
document.write( "($ understood)<BR>\n" );
document.write( "x>y-------------------eq1<BR>\n" );
document.write( "and<BR>\n" );
document.write( "0.25x+0.10y=2.15 multiply each term by 100 and divide by each term by 5 (get rid of decimals and reduce size) :<BR>\n" );
document.write( "5x+2y=43 solve for y<BR>\n" );
document.write( "2y=43-5x<BR>\n" );
document.write( "y=(43-5x)/2----------------------eq2<BR>\n" );
document.write( "Now we know that the number of dimes and quarters has to be positive numbers as well as whole numbers<BR>\n" );
document.write( "Looking at eq2, we see that x has to be less than or equal to 8, otherwise the <BR>\n" );
document.write( "number of dimes will be negative<BR>\n" );
document.write( "But x cannot be 8--that would make the number of dimes a fraction(3/2)<BR>\n" );
document.write( "How about 7 for x?  Then y=(43-35)/2=4<BR>\n" );
document.write( "7 quarters and 4 dimes fill the requirement of eq1, but does this add up to $2.15?<BR>\n" );
document.write( "$1.75+$0.40=$2.15---------------This is a solution. Are there others??<BR>\n" );
document.write( "How about 6 for x?----No good, y is a fraction<BR>\n" );
document.write( "How about 5 for x? ---Then y=(43-25)/2=9  No good because the requirement of eq1 is not satisfied even though these add up to $2.15<BR>\n" );
document.write( "And anything smaller than 5 will make y>x<BR>\n" );
document.write( "Ans: 7 quarters; 4 dimes=D --11 coins\r<BR>\n" );
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document.write( "Hope this helps---ptaylor </SPAN>\n" );
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