document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=95442>Question 95442</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, this word probelm is really challenging me and I was wondering if you could help. The problem is<BR>\n" );
document.write( " \"A test has twenty questions worth 100 points. The test consists of True/False questions worth 3 points each and multiple-choice questions worth 11points each. How many multiple choice questions are on the test?\"<BR>\n" );
document.write( "   Thanks sooo much! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #69459 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=69459\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let T represent the number of True/False questions and let M represent the number of Multiple<BR>\n" );
document.write( "Choice questions.<BR>\n" );
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document.write( "Since the total number of questions is 20 we know that the number of True/False questions<BR>\n" );
document.write( "plus the number of Multiple Choice questions is equal to 20. In equation form this is:<BR>\n" );
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document.write( "T + M = 20 <=== remember this. It is equation 1.<BR>\n" );
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document.write( "Since True/False questions are worth 3 points, the number of points you could score on<BR>\n" );
document.write( "these questions is T times 3 points or 3*T. And since the Multiple Choice questions <BR>\n" );
document.write( "are worth 11 points each, the number of points you could score on these questions is M times<BR>\n" );
document.write( "11 points or 11*M. Now if we add up the total number of points possible, the result is<BR>\n" );
document.write( "100 points. In equation form this becomes:<BR>\n" );
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document.write( "3T + 11M = 100 <=== this is equation 2<BR>\n" );
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document.write( "Now let's return to equation 1 and subtract M from both sides. When we do this subtraction<BR>\n" );
document.write( "the +M disappears from the left side and the equation becomes:<BR>\n" );
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document.write( "T = 20 - M<BR>\n" );
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document.write( "Then we can go to equation 2 and for T in that equation we can substitute 20 - M . This<BR>\n" );
document.write( "substitution makes the second equation become:<BR>\n" );
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document.write( "3(20 - M) + 11M = 100<BR>\n" );
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document.write( "Do the distributed multiplication on the left side by multiplying 3 times each of the<BR>\n" );
document.write( "terms in the parentheses to get:<BR>\n" );
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document.write( "60 - 3M + 11M = 100<BR>\n" );
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document.write( "Get rid of the 60 on the left side by subtracting 60 from both sides. This results in:<BR>\n" );
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document.write( "-3M + 11M = 40<BR>\n" );
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document.write( "Then combine the two terms on the left side by combining -3M and + 11M to get +8M and<BR>\n" );
document.write( "this reduces the equation to:<BR>\n" );
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document.write( "8M = 40<BR>\n" );
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document.write( "Solve for M by dividing both sides of this equation by 8 ... the multiplier of M to get:<BR>\n" );
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document.write( "M = 40/8 = 5<BR>\n" );
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document.write( "This tells us that there are 5 Multiple Choice questions. So the remaining 15 questions<BR>\n" );
document.write( "on the test must be True/False questions.<BR>\n" );
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document.write( "Check. If we got all 5 Multiple Choice questions correct we would score 11 points for<BR>\n" );
document.write( "each of the five questions and this would give us 55 points. Then if we got all 15 True/False<BR>\n" );
document.write( "questions correct at 3 points each, we would score 15 times 3 or 45 points. So the total<BR>\n" );
document.write( "number of points on the test would be 55 + 45 = 100. This is the correct number of points<BR>\n" );
document.write( "on the test so our answer is correct ... 5 Multiple Choice questions and 15 True/False<BR>\n" );
document.write( "questions.<BR>\n" );
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document.write( "Hope this helps you to understand the problem and a way that you can solve it by writing two<BR>\n" );
document.write( "equations from the information given in the problem.<BR>\n" );
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document.write( " </SPAN>\n" );
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