document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1169673>Question 1169673</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The business partners, A, B and C, share the profit as follows:<BR>\n" );
document.write( "The ratio of A's share to B is 6:5 and the ration of B's share to C is 3:4. Determine:<BR>\n" );
document.write( "1.1 A's share: B's share: C's share<BR>\n" );
document.write( "1.2 the total profit if A gets $5000 less than C </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #794471 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=794471\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Part (1)\r<BR>\n" );
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document.write( "The ratio of A to B is 6:5<BR>\n" );
document.write( "The ratio of B to C is 3:4\r<BR>\n" );
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document.write( "Let's write the ratios together with arrows connecting them like so <BR>\n" );
document.write( "6:5  <--> 3:4\r<BR>\n" );
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document.write( "The goal is to get the inner values 5 and 3 to match up and be the same number. \r<BR>\n" );
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document.write( "What we can do is multiply both parts of the first ratio by some number x<BR>\n" );
document.write( "6:5 turns into 6x:5x\r<BR>\n" );
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document.write( "Similarly,<BR>\n" );
document.write( "3:4 turns into 3y:4y<BR>\n" );
document.write( "for some number y\r<BR>\n" );
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document.write( "The LCM of 5 and 3 is 15, so if x = 3 and y = 5, then we get<BR>\n" );
document.write( "6x:5x = 6*3:5*3 = 18:15<BR>\n" );
document.write( "3y:4y = 3*5:4*5 = 15:20\r<BR>\n" );
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document.write( "In short, we found that<BR>\n" );
document.write( "6:5 is equivalent to 18:15 <BR>\n" );
document.write( "3:4 is equivalent to 15:20 \r<BR>\n" );
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document.write( "Then looking at <BR>\n" );
document.write( "18:15 <--> 15:20<BR>\n" );
document.write( "we see the inner values are 15 each\r<BR>\n" );
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document.write( "We can then link the two new ratios<BR>\n" );
document.write( "18:15 <--> 15:20 becomes 18:15:20\r<BR>\n" );
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document.write( "Answer = 18:15:20\r<BR>\n" );
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document.write( "Part (2)\r<BR>\n" );
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document.write( "Let m be some positive number\r<BR>\n" );
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document.write( "The ratio 18:15:20 means<BR>\n" );
document.write( "A's share = 18m<BR>\n" );
document.write( "B's share = 15m<BR>\n" );
document.write( "C's share = 20m\r<BR>\n" );
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document.write( "So basically 18m:15m:20m is equivalent to 18:15:20 if we divide all parts by m.\r<BR>\n" );
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document.write( "Person A gets $5000 less compared to C, so,<BR>\n" );
document.write( "A = C - 5000<BR>\n" );
document.write( "18m = 20m - 5000<BR>\n" );
document.write( "18m-20m  = -5000<BR>\n" );
document.write( "-2m = -5000<BR>\n" );
document.write( "m = -5000/(-2)<BR>\n" );
document.write( "m = 2500\r<BR>\n" );
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document.write( "The total profit is<BR>\n" );
document.write( "A+B+C = 18m+15m+20m <BR>\n" );
document.write( "A+B+C = 53m<BR>\n" );
document.write( "A+B+C = 53*2500<BR>\n" );
document.write( "A+B+C = 132,500 dollars\r<BR>\n" );
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document.write( "Or you can calculate the individual shares <BR>\n" );
document.write( "A = 18m = 18*2500 = 45,000<BR>\n" );
document.write( "B = 15m = 15*2500 = 37,500<BR>\n" );
document.write( "C = 20m = 20*2500 = 50,000<BR>\n" );
document.write( "which adds up to<BR>\n" );
document.write( "A+B+C = 45,000+37,500+50,000 = 132,500<BR>\n" );
document.write( "which is the same value we got earlier.\r<BR>\n" );
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document.write( "Answer = Total profit is 132,500 dollars<BR>\n" );
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