document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1206870>Question 1206870</A>: <I><SPAN STYLE=\"word-break: break-all;\"> There were 5/7 as many red marbles as blue marbles in a jar. Dave took some blue marbles out of the jar and replaced them with the same number of red marbles. The number of red marbles became 5/9 of all the marbles in the jar. Which of the following is a possible number of blue marbles that were replaced? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #844576 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=844576\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Note that it is hard to know how to answer the question, since you didn't provide the answer choices.<br><BR>\n" );
document.write( "But we can do some analysis to determine what kind of answers are possible.<br><BR>\n" );
document.write( "Initially the number of red marbles was 5/7 the number of blue marbles.  That means that the red marbles were 5/12 of the total and the blue marbles were 7/12 of the total.<br><BR>\n" );
document.write( "Let x be the total number of marbles.  Then (5/12)x is the original number of red marbles.<BR>\n" );
document.write( "Let y be the number of blue marbles that were removed and replaced with red marbles.<br><BR>\n" );
document.write( "After the change, the number of red marbles was 5/9 of the total number:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%2F12%29x%2By=%285%2F9%29x ALIGN=MIDDLE  ALT=\"%285%2F12%29x%2By=%285%2F9%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%285%2F9%29x-%285%2F12%29x=%2820%2F36%29x-%2815%2F36%29x=%285%2F36%29x ALIGN=MIDDLE  ALT=\"y=%285%2F9%29x-%285%2F12%29x=%2820%2F36%29x-%2815%2F36%29x=%285%2F36%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "x and y are whole numbers.  Since y=(5/36)x, the total number of marbles must be a multiple of 36, and the number of blue marbles that were removed and replaced with red marbles must be a multiple of 5.<br><BR>\n" );
document.write( "There is not enough information to find a single possible answer for the number of blue marbles that were removed and replaced with red marbles.  But we do know that...<br><BR>\n" );
document.write( "ANSWER: any number that is a multiple of 5<br><BR>\n" );
document.write( "Some possible sets of numbers for the problem....<br><BR>\n" );
document.write( "36 total marbles; originally 15 red and 21 blue; 5 marbles changed to give 20 red and 16 blue; 20/(20+16) = 20/36 = 5/9<br><BR>\n" );
document.write( "72 total; originally 30 and 42; 10 change to give 40 and 32; 40/(40+32) = 40/72 = 5/9<br><BR>\n" );
document.write( "etc....<br> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );