document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=894859>Question 894859</A>: <I><SPAN STYLE=\"word-break: break-all;\"> This question is in the ratios & proportions section of the book. The problem is that there are no instructions or examples. I would be grateful if I could get a detailed answer so that I know how to complete the other questions like this. \r<BR>\n" );
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document.write( "Set up the proportion:<BR>\n" );
document.write( "Set up the two ratios and write your equation, choosing an appropriate variable for the bear population. <BR>\n" );
document.write( "Bear population. To estimate the size of the bear population on the Keweenaw Peninsula, conservationists captured, tagged, and released 50 bears. One year later, a random sample of 100 bears included only 2 tagged bears. What is the conservationist's estimate of the size of the bear population?\r<BR>\n" );
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document.write( "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 #542386 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=542386\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a random sample of 50 bears were tagged and released.<BR>\n" );
document.write( "one year later they took a random sample of 100 bears.<BR>\n" );
document.write( "2 of them were tagged and the rest were not.\r<BR>\n" );
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document.write( "all things being equal, they determined that the number of bears must have been 50 / 2 * 100 = 2500.\r<BR>\n" );
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document.write( "here's how they did it and why.\r<BR>\n" );
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document.write( "they took a sample of 50 and tagged them all.\r<BR>\n" );
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document.write( "this 50 was out of an unknown number of bears in the population.\r<BR>\n" );
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document.write( "they assigned x to represent the number of bears in the population.\r<BR>\n" );
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document.write( "they got a ratio of 50 / x.\r<BR>\n" );
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document.write( "that's 50 tagged bears out of x bears.\r<BR>\n" );
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document.write( "when they took another sample of 100 bears and found that 2 were tagged, they now had a sample where they knew the number of tagged bears in relationship to the number of total bears.\r<BR>\n" );
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document.write( "all things being equal, this sample should have the same ratio as the original sample.\r<BR>\n" );
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document.write( "the original sample was 50/x\r<BR>\n" );
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document.write( "this sample was 2/100\r<BR>\n" );
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document.write( "they set the ratios equal to each other and they got 50/x = 2/100\r<BR>\n" );
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document.write( "they cross multiplied to get 2x = 50*100\r<BR>\n" );
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document.write( "they divided both sides of the equation by 2 to get x = 50*100/2.\r<BR>\n" );
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document.write( "they solved for x to get x = 2500.\r<BR>\n" );
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document.write( "they estimated that the bear population was somewhere around 2500 based on this sample.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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