document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=793048>Question 793048</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Kat spends 30 minutes of time partly in listening to her professor and partly in text messaging her close friends. The time she spends on text messaging is 2 times more than what she spends listening to her professor. How many minutes does Kat spend listening to her professor? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #843725 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=843725\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The answer shown by the other tutor is very probably the intended answer to the problem.  However, it is the wrong answer, because very probably the problem was written incorrectly.<br><BR>\n" );
document.write( "Any math problem written using any form of a phrase like \"2 times more than\" is an invalid problem, because nearly everybody interprets that phrase incorrectly.<br><BR>\n" );
document.write( "If I spend 2 TIMES AS MUCH time on one task as I do on another, then the amount of time I spend on one task can be represented by x, and the time I spend on the other task can then be represented as 2x.<br><BR>\n" );
document.write( "But if I spend 2 TIMES MORE on one task as I do on another, and the amount of time I spend on the shorter task is x, then the amount of time I spend on the longer task is the amount of time I spend on the shorter task, PLUS 2 TIMES MORE that amount of time -- i.e., x + 2x = 3x.<br><BR>\n" );
document.write( "In everyday sloppy language, \"2 times as much as\" and \"2 times more than\" are used to mean the same thing, but they do not.<br><BR>\n" );
document.write( "With the grammatically correct interpretation of the question as written....<br><BR>\n" );
document.write( "x = amount of time spent listening to her professor<BR>\n" );
document.write( "3x = amount of time spent text messaging<br><BR>\n" );
document.write( "The total time is 30 minutes:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B3x=30 ALIGN=MIDDLE  ALT=\"x%2B3x=30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x=30 ALIGN=MIDDLE  ALT=\"4x=30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=7.5 ALIGN=MIDDLE  ALT=\"x=7.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "(correct) ANSWER: Kat spends 7.5 minutes listening to her professor<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );