document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1173116>Question 1173116</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Jonathan counts the change in his piggy bank.  He has $ 17 in 10 ¢ and 25 ¢ coins.<BR>\n" );
document.write( "Knowing that there are 3 times more 25 ¢ coins than 10 ¢ coins,<BR>\n" );
document.write( "how many 10 ¢ and 25 ¢ coins are in the piggy bank? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #798261 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</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=798261\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Faulty statement of the problem.<br><BR>\n" );
document.write( "It is most likely not your fault -- you probably showed the problem exactly as it was given to you.  However, as shown, the problem has no solution in whole numbers, so it is flawed.<br><BR>\n" );
document.write( "Unfortunately, in everyday English, the phrases \"3 times more than\" and \"3 times as many as\" are sloppily used to mean the same thing, but they do not.  3 times AS MANY AS x is 3x; 3 times MORE THAN x is x, plus 3x MORE, which is x+3x = 4x.<br><BR>\n" );
document.write( "If we try to solve the problem as given, then....<br><BR>\n" );
document.write( "x = number of 10 cent coins<BR>\n" );
document.write( "4x = number of 25 cent coins<br><BR>\n" );
document.write( "Total value is $17, or 1700 cents:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2810%29%2B4x%2825%29+=+1700 ALIGN=MIDDLE  ALT=\"x%2810%29%2B4x%2825%29+=+1700\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10x%2B100x+=+1700 ALIGN=MIDDLE  ALT=\"10x%2B100x+=+1700\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=110x+=+1700 ALIGN=MIDDLE  ALT=\"110x+=+1700\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+1700%2F110 ALIGN=MIDDLE  ALT=\"x+=+1700%2F110\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "That calculation does not yield a whole number value for x.<br><BR>\n" );
document.write( "If you correct the wording of the problem to say that there are 3 times AS MANY 25 cent coins as 10 cent coins, then the problem has a reasonable solution.<br><BR>\n" );
document.write( "x = number of 10 cent coins<BR>\n" );
document.write( "3x = number of 25 cent coins<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2810%29%2B3x%2825%29+=+1700 ALIGN=MIDDLE  ALT=\"x%2810%29%2B3x%2825%29+=+1700\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "...<br><BR>\n" );
document.write( "You can finish from there.<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );