document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1187751>Question 1187751</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this (it is based on matrices as there was no option to select that I chose word problems only):<BR>\n" );
document.write( "Statistics show that at a certain university, 70% of the students who live on campus during a given semester will remain on campus the following semester, and 90% of students living off campus during a given semester will remain off campus the following semester. Let x and y denote the number of students who live on and off campus this semester, and let u and v be the corresponding numbers for the next semester. Then,<BR>\n" );
document.write( " 0 . 7 x + 0 . 1 y = u<BR>\n" );
document.write( "0.3x + 0.9y = v<BR>\n" );
document.write( "(a) Write this system of equations in matrix form.<BR>\n" );
document.write( "(b) Solve the resulting matrix equation for [x<BR>\n" );
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document.write( "(c) Suppose that, out of a group of 9000 students, 6000 currently live on campus and 3000 live off campus. How many lived on campus last semester? How many will live off campus next semester? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #819225 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=819225\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> for part c, i get the following:\r<BR>\n" );
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document.write( "6000 currently live on campus and 3000 currently live off campus.\r<BR>\n" );
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document.write( "since x is the number who live on campus this semester and y is the number who currrently live off campus this summer, then you get:\r<BR>\n" );
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document.write( "x = 6000 and y = 3000.\r<BR>\n" );
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document.write( "your first equation is the ones who will be living on campus next semester.\r<BR>\n" );
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document.write( "of the 6000 that are currently living on campus, 70% will still live on campus next semester.<BR>\n" );
document.write( "of the 3000 that are currently living off campus, 10% will be living on campus next semester.<BR>\n" );
document.write( ".7x + .1y = u becomes .7*6000 + .1*3000 = 4500 that will be living on campus next semeste.\r<BR>\n" );
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document.write( "your second equation is the ones who will be living off campus next semeste.\r<BR>\n" );
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document.write( "of the 6000 that are currently living on campus, 30% will live off campus next semester.<BR>\n" );
document.write( "of the 3000 that are currently living off campus, 90% will continue to live off campus next semester.<BR>\n" );
document.write( ".3x + .9y = v becomes .3*6000 + .9*3000 = 4500 that will be living off campus next semester.\r<BR>\n" );
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document.write( "for part a i get the following:\r<BR>\n" );
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document.write( "the matrix is:\r<BR>\n" );
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document.write( "tableau 1 row 1 equals            .7              .1              u\r\n" );
document.write( "tableau 1 row 2 equals            .3              .9              v\r\n" );
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document.write( "</PRE>\r<BR>\n" );
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document.write( "normally, u and v would be constants.<BR>\n" );
document.write( "since i didn't know their value up front (i learaned it in part c), i left them as u and v.\r<BR>\n" );
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document.write( "for part b, i get the following:\r<BR>\n" );
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document.write( "start with:\r\n" );
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document.write( "tableau 1 row 1 equals            .7              .1              u\r\n" );
document.write( "tableau 1 row 2 equals            .3              .9              v\r\n" );
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document.write( "tableau 2 row 1 equals 9 * tableau 1 row 1 minus tableau 1 row 2.\r\n" );
document.write( "tableau 2 row 2 equals tableau 1 row 2.\r\n" );
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document.write( "you get:\r\n" );
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document.write( "tableau 2 row 1 equals           6                0              9u - v\r\n" );
document.write( "tableau 2 row 2 equals          .3               .9              v\r\n" );
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document.write( "tableau 3 row 1 equals tableau 2 row 1\r\n" );
document.write( "tableau 3 row 2 = tableau 2 row 2 minus .05 * tableau 2 row 1.\r\n" );
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document.write( "you get:\r\n" );
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document.write( "tableau 3 row 1 equals           6                0              9u - v\r\n" );
document.write( "tableau 3 row 2 equals           0               .9             v - .45u + .05v\r\n" );
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document.write( "tableau 4 row 1 equals tableau 3 row 1 divided by 6.\r\n" );
document.write( "tableau 4 row 2 equals tableau 3 row 2 divided by .9.\r\n" );
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document.write( "you get:\r\n" );
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document.write( "tableau 4 row 1 equals          1                0            (9u - v) / 6\r\n" );
document.write( "tableau 4 row 2 equals          0                1            (1.05v - .45u) / .9\r\n" );
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document.write( "</PRE>\r<BR>\n" );
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document.write( "that completes part b.\r<BR>\n" );
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document.write( "from part c, we know that both u and v = 4500 each.\r<BR>\n" );
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document.write( "to confirm part b was done correctly, replace u and v with 4500 to get:\r<BR>\n" );
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document.write( "tableau 4 row 1 equals          1                0     (9*4500-4500)/6 = 6000\r\n" );
document.write( "tableau 4 row 2 equals          0                1     (1.05*4500 - .45*4500) / .9 = 3000\r\n" );
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document.write( "</PRE>\r<BR>\n" );
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document.write( "since we already know that x was equal to 6000 and y was equal to 3000 because that was given to us, this confirms the matrix equation was modeled correctly.\r<BR>\n" );
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document.write( "i believe this satisfies the requirements for this problem.<BR>\n" );
document.write( "let me know if you have any questions.\r<BR>\n" );
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document.write( "solving part c first helped me in analyzing parts a and b because i had some number to check my answers for part a and b against.\r<BR>\n" );
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document.write( "here's a reference on matrix operations you might find helpful.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"https://www.studypug.com/algebra-help/the-three-types-of-matrix-row-operations?camp_id=1026250253&grp_id=112411027342&kw=&mt=&source=g&pos=&tgt=dsa-19959388920&loc=9003567&device=c&adid=529422243034&gclid=EAIaIQobChMItIvzlf-59AIVg2pvBB3u6wjTEAMYAiAAEgLzxPD_BwE\" target = \"_blank\">https://www.studypug.com/algebra-help/the-three-types-of-matrix-row-operations?camp_id=1026250253&grp_id=112411027342&kw=&mt=&source=g&pos=&tgt=dsa-19959388920&loc=9003567&device=c&adid=529422243034&gclid=EAIaIQobChMItIvzlf-59AIVg2pvBB3u6wjTEAMYAiAAEgLzxPD_BwE</a>\r<BR>\n" );
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document.write( "theo\r<BR>\n" );
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document.write( " </SPAN>\n" );
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