document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1205318>Question 1205318</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Siti has RM450000 in her ASB. She wants to invest in Gading Mutual deposit, Maju<BR>\n" );
document.write( "Makmur bar gold, Indah certificate deposit and Selamat Maju bar gold which pay<BR>\n" );
document.write( "simple annual interest of 9%, 6%, 10% and 15%, respectively. Moreover, she wants<BR>\n" );
document.write( "to combine annual return of 8% and want to have only one-third of investment in<BR>\n" );
document.write( "Indah certificate deposit and Selamat Maju bar gold.<BR>\n" );
document.write( "a. Write the linear model system equation for the whole investment.<BR>\n" );
document.write( "c. Use elimination method to find each of the investment\r<BR>\n" );
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document.write( "3. Alia rows a boat upstream from one point on a river to another point 4 km away in 1.5 hours.<BR>\n" );
document.write( "The return trip, traveling with the current, takes only 45 min.<BR>\n" );
document.write( "a. Identify the variables involve in algebra.<BR>\n" );
document.write( "b. Find the speed of the current flowing by using back-substitution method </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #842037 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=842037\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i'll do number 3 for you.<BR>\n" );
document.write( "you can then resubmit for the first one in a separate request.<BR>\n" );
document.write( "if i can, i'll solve that one as well, but i'm not sure i can do it, at this time.<BR>\n" );
document.write( "i do have one question on the first part.<BR>\n" );
document.write( "did you mean that one third of the investment should be in indah and one third of the investment should be in selamat, or did you mean that one third of the investment should be in the sum of (indah and selamat).\r<BR>\n" );
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document.write( ". Alia rows a boat upstream from one point on a river to another point 4 km away in 1.5 hours.<BR>\n" );
document.write( "The return trip, traveling with the current, takes only 45 min.<BR>\n" );
document.write( "a. Identify the variables involve in algebra.<BR>\n" );
document.write( "b. Find the speed of the current flowing by using back-substitution method\r<BR>\n" );
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document.write( "the formula i normally use with these is (rate of boat plus or minus rate of current) * time = distance.\r<BR>\n" );
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document.write( "let r = rate of the boat, c = rate of the current, t = time, d = distance.<BR>\n" );
document.write( "formula becomes (r +/- c) * t = d\r<BR>\n" );
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document.write( "going upstream, the formula becomes (r - c) * 1.5 = 4<BR>\n" );
document.write( "going downstream, the formula becomes (r + c) * .75 = 4\r<BR>\n" );
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document.write( "the time is in hours.<BR>\n" );
document.write( "the distance is in kilometers.\r<BR>\n" );
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document.write( "the back substitution says solve for one of the variables and use the value of that to solve for the other variable.\r<BR>\n" );
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document.write( "your two equations to solve simultaneously are:<BR>\n" );
document.write( "(r - c) * 1.5 = 4<BR>\n" );
document.write( "(r + c) * .75 = 4\r<BR>\n" );
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document.write( "we'll solve for c first.\r<BR>\n" );
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document.write( "simplify both equations to get:\r<BR>\n" );
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document.write( "1.5 * r - 1.5 * c = 4<BR>\n" );
document.write( ".75 * r + .75 * c = 4\r<BR>\n" );
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document.write( "in the second equation, solve for c to get:<BR>\n" );
document.write( "c = (4 - .75 * r) / .75\r<BR>\n" );
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document.write( "in the first equation, replace c with that to get:<BR>\n" );
document.write( "1.5 * r - 1.5 * c = 4 becomes:<BR>\n" );
document.write( "1.5 * r - 1.5 * (4 - .75 * r) / .75 = 4<BR>\n" );
document.write( "multiply both sides of the equation by .75 to get:<BR>\n" );
document.write( "1.5 * .75 * r - 1.5 * (4 - .75 * r) = 4 * .75<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "1.125 * r - 6 + 1.125 * r = 3<BR>\n" );
document.write( "combine like terms to get:<BR>\n" );
document.write( "2.25 * r - 6 = 3<BR>\n" );
document.write( "add 6 to both sides of the equation to get\"<BR>\n" );
document.write( "2.25 * r = 9<BR>\n" );
document.write( "solve for r to get:<BR>\n" );
document.write( "r = 4\r<BR>\n" );
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document.write( "go back to your original equations and replace r with 4 to get:<BR>\n" );
document.write( "(r - c) * 1.5 = 4 becomes (4 - c) * 1.5 = 4<BR>\n" );
document.write( "(r + c) * .75 = 4 becomes (4 + c) * .75 = 4<BR>\n" );
document.write( "simplify each equation to get:<BR>\n" );
document.write( "6 - 1.5 * c = 4<BR>\n" );
document.write( "3 + .75 * c = 4<BR>\n" );
document.write( "subtract 6 from both sides of the first equation and subtract 3 from both sides of the second equation to get:<BR>\n" );
document.write( "-1.5 * c = -2<BR>\n" );
document.write( ".75 *c = 1<BR>\n" );
document.write( "solve for c in both equations to get:<BR>\n" );
document.write( "c = 1.33333.....<BR>\n" );
document.write( "c = 1.33333.....\r<BR>\n" );
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document.write( "you now have r = 4 and c = 1.3333....<BR>\n" );
document.write( "since 1.3333..... is the same as 4/3, you now have:<BR>\n" );
document.write( "r = 4 and c = 4/3.\r<BR>\n" );
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document.write( "confirm by replacing r with 4 and c with 4/3 in the original two equations to get:<BR>\n" );
document.write( "(r - c) * 1.5 = 4 becomes (4 - 4/3) * 1.5 = 4<BR>\n" );
document.write( "(r + c) * .75 = 4 becomes (4 + 4/3) * .75 = 4<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "8/3 * 1.5 = 4 becomes 4 = 4<BR>\n" );
document.write( "16/3 * .75 = 4 becomes 4 = 4<BR>\n" );
document.write( "this confirms the solution is correct.\r<BR>\n" );
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document.write( "the solution is that the rate of the current = 4/3 kilometers per hour which is the same as 1.333333.... kilometers per hour which is the same as 1.33 kilometers per hour when you round to 2 decimal places.\r<BR>\n" );
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document.write( "that should take care of number 3.<BR>\n" );
document.write( "if you're happy with the solution, then resubmit your request with just the first part so somebody can take a look at that.\r<BR>\n" );
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document.write( "in the future, you should only submit one problem per request.<BR>\n" );
document.write( "i believe that's in the guidelines and i have seen other tutors request the same from other students.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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