document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1206890>Question 1206890</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 become 5/9 of all the marbles in the jar. Which of the following is a possible number of blue marbles that were replaced.<BR>\n" );
document.write( "1) 9<BR>\n" );
document.write( "2) 10<BR>\n" );
document.write( "3) 36<BR>\n" );
document.write( "4) 63\r<BR>\n" );
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document.write( "Problem with answer choices </SPAN>\n" );
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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( "Only one of the answer choices is a multiple of 5.<br><BR>\n" );
document.write( "ANSWER: 2) 10<br><BR>\n" );
document.write( "The 10 blue marbles that were removed and replaced with red marbles are 5/36 of the total number of marbles<BR>\n" );
document.write( "So the total number of marbles was 72<BR>\n" );
document.write( "Originally the red marbles were 5/12 of the total, so there were 30 red marbles and 42 blue<BR>\n" );
document.write( "After the exchange there were 40 red marbles and 32 blue<BR>\n" );
document.write( "In the end the red marbles were 40/72 = 5/9 of the total<br><BR>\n" );
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