document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=76379>Question 76379</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Y=A/X<BR>\n" );
document.write( "2< or = X < or = 6<BR>\n" );
document.write( "4/3 < or = Y < = B\r<BR>\n" );
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document.write( "A=?<BR>\n" );
document.write( "B=?<BR>\n" );
document.write( " I have that x=4 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #54805 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=54805\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You are given that:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y+=+A%2FX ALIGN=MIDDLE  ALT=\"Y+=+A%2FX\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "with the restrictions that<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%3C=X%3C=6 ALIGN=MIDDLE  ALT=\"2%3C=X%3C=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%2F3%29%3C=y%3C=B ALIGN=MIDDLE  ALT=\"%284%2F3%29%3C=y%3C=B\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The problem is to find the value of both A and B<BR>\n" );
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document.write( "Go to the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y+=+A%2FX ALIGN=MIDDLE  ALT=\"Y+=+A%2FX\"   DISABLED_style= \"max-width:90%; height:auto;\" > and let's solve for the range of Y based on the domain<BR>\n" );
document.write( "of values that X can take.  From the restrictions on X we know that the smallest value <BR>\n" );
document.write( "that X can take is 2 and the largest value that X can take is 6.  We will use these <BR>\n" );
document.write( "two values to find the smallest and largest values that Y can be based on the values<BR>\n" );
document.write( "of X.  <BR>\n" );
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document.write( "If X is the smallest value it can be (2) then Y is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y+=+A%2F2 ALIGN=MIDDLE  ALT=\"Y+=+A%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "If X is the largest value it can be (6) then Y is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y+=+A%2F6 ALIGN=MIDDLE  ALT=\"Y+=+A%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now notice that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%2F6 ALIGN=MIDDLE  ALT=\"A%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > is smaller than <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%2F2 ALIGN=MIDDLE  ALT=\"A%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > because the larger the denominator<BR>\n" );
document.write( "the smaller the value of the fraction.  Therefore, the larger that X gets, the smaller that<BR>\n" );
document.write( "Y will be.  <BR>\n" );
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document.write( "So we can say that the smallest Y can be is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%2F6 ALIGN=MIDDLE  ALT=\"A%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the largest Y can be is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%2F2 ALIGN=MIDDLE  ALT=\"A%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "This can be translated to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%2F6+%3C=+Y+%3C=+A%2F2 ALIGN=MIDDLE  ALT=\"A%2F6+%3C=+Y+%3C=+A%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "Compare this to what limits on Y the problem gave ... <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F3%3C=Y%3C=B ALIGN=MIDDLE  ALT=\"4%2F3%3C=Y%3C=B\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now compare the left half of these two inequalities for Y and you can see that:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%2F6+=+4%2F3 ALIGN=MIDDLE  ALT=\"A%2F6+=+4%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Solve this proportion by cross-multiplying the numerator of the left side by the denominator<BR>\n" );
document.write( "of the right side. Then multiply the denominator of the left side times the numerator <BR>\n" );
document.write( "of the right side. Then set these two products equal.  If you do this to this problem,<BR>\n" );
document.write( "the two products are 3A and 24.  Set them equal and you get 3A = 24. Solve for A by dividing<BR>\n" );
document.write( "both sides by 3 and you get A = 8.  That's one of the terms you were to find.  <BR>\n" );
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document.write( "Now compare the right sides of the two inequalities we have for Y.  For them to be equivalent<BR>\n" );
document.write( "you have to have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%2F2+=+B ALIGN=MIDDLE  ALT=\"A%2F2+=+B\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  But you now know that A = 8.  Substitute 8 for A and <BR>\n" );
document.write( "you get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2F2+=+B ALIGN=MIDDLE  ALT=\"8%2F2+=+B\"   DISABLED_style= \"max-width:90%; height:auto;\" > and this simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B+=+4 ALIGN=MIDDLE  ALT=\"B+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  <BR>\n" );
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document.write( "So the two answers you need are A = 8 and B = 4.<BR>\n" );
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document.write( "Hope that you can follow the above process and that it is understandable. The cross-multiplying<BR>\n" );
document.write( "method of solving proportions is a method that can be used for all proportions, not just <BR>\n" );
document.write( "for the one in this problem. </SPAN>\n" );
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