document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=84355>Question 84355</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/1565771400/algebrahomeworkh>Algebra 2 An incremental Development</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> We need help.  My daughter has been working on this problem all weekend and we still do not get the right answer.  We are working on inverse variation as a ratio.  The problem is :  The ratio of acrobats in blue to acrobats in pink was 4 to 5.  Those who wore blue numbered 1200 fewer than twice the number who wore pink.  How many wore blue, and how many wore pink?  All help is appreciated.  Thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #60760 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=60760\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First, let B represent the number of acrobats wearing blue.  Also let P represent the number<BR>\n" );
document.write( "of acrobats wearing pink.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Two times the number of acrobats wearing pink is, therefore, 2*P<BR>\n" );
document.write( ".<BR>\n" );
document.write( "1200 less that that is 2*P - 1200 and that is equal to the number of acrobats wearing<BR>\n" );
document.write( "blue. So we can write that B = 2*P - 1200<BR>\n" );
document.write( ".<BR>\n" );
document.write( "So we can write the ratio of blue to pink acrobats as:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B%2FP+=+%282%2AP-1200%29%2FP ALIGN=MIDDLE  ALT=\"B%2FP+=+%282%2AP-1200%29%2FP\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "But you were told in the problem that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B%2FP+=+4%2F5 ALIGN=MIDDLE  ALT=\"B%2FP+=+4%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Substitute this into the ratio<BR>\n" );
document.write( "equation to get:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F5+=+%282%2AP+-1200%29%2FP ALIGN=MIDDLE  ALT=\"4%2F5+=+%282%2AP+-1200%29%2FP\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "An easy way to work on this proportion (a fraction on the opposite sides of the equal sign)<BR>\n" );
document.write( "is to cross multiply ... that is multiply the numerator on the left side by the denominator<BR>\n" );
document.write( "on the right side and set this product equal to the product you get by multiplying<BR>\n" );
document.write( "the numerator on the right side by the denominator on the left side. For this problem<BR>\n" );
document.write( "that translates to multiplying 4 by P and setting that equal to  multiplying (2*P - 1200)<BR>\n" );
document.write( "by 5.  This gives you the equation:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2AP+=+%282%2AP+-+1200%29%2A5 ALIGN=MIDDLE  ALT=\"4%2AP+=+%282%2AP+-+1200%29%2A5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Multiply out the right side and the equation becomes:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2AP+=+10%2AP+-+6000 ALIGN=MIDDLE  ALT=\"4%2AP+=+10%2AP+-+6000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "To get the P terms on the same side of the equation subtract 10P from both sides of the <BR>\n" );
document.write( "equation.  This results in:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6%2AP+=+-6000 ALIGN=MIDDLE  ALT=\"-6%2AP+=+-6000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Solve for P by dividing both sides of the equation by -6 which is the multiplier of P.<BR>\n" );
document.write( "When you do this division, the result is:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P+=+1000 ALIGN=MIDDLE  ALT=\"P+=+1000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "You now know that there are 1000 acrobats in pink.  Since the ratio of Blue to Pink is 4 to 5,<BR>\n" );
document.write( "you can write:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F5+=+B%2F1000 ALIGN=MIDDLE  ALT=\"4%2F5+=+B%2F1000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Using the cross product process just as before results in:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2A1000+=+B%2A5 ALIGN=MIDDLE  ALT=\"4%2A1000+=+B%2A5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Dividing both sides by 5 results in:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B+=+%284%2A1000%29%2F5+=+4000%2F5+=+800 ALIGN=MIDDLE  ALT=\"B+=+%284%2A1000%29%2F5+=+4000%2F5+=+800\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "So there are 800 acrobats dressed in blue and 1000 acrobats dressed in pink.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Check ... twice the acrobats dressed in pink is 2000. Notice that the number dressed in<BR>\n" );
document.write( "blue is 2000 - 800 = 1200 less than that number.  That checks.  And the ratio of 800 acrobats <BR>\n" );
document.write( "in blue to 1000 in pink is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=800%2F1000 ALIGN=MIDDLE  ALT=\"800%2F1000\"   DISABLED_style= \"max-width:90%; height:auto;\" > and that reduces to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F5 ALIGN=MIDDLE  ALT=\"4%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > so it also checks.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Hope this helps you to see how to work the problem. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );