document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=21508>Question 21508</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Here is my problem:\r<BR>\n" );
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document.write( "A father and his two sons bought a drug store for $320,000. If the father<BR>\n" );
document.write( "invested twice as much as the older son, and the older son invested<BR>\n" );
document.write( "$45,000 less than twice the younger son, how much did the father and <BR>\n" );
document.write( "his sons each invest?\r<BR>\n" );
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document.write( "This needs to be solved as a linear equation.<BR>\n" );
document.write( "The answer is: younger son, $65,000; older son, $85,000; father $170,000\r<BR>\n" );
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document.write( "I started with:<BR>\n" );
document.write( "Father = A, older son = B and younger son = C<BR>\n" );
document.write( "A + B + C = 320,000<BR>\n" );
document.write( "2B = A<BR>\n" );
document.write( "2C - 45,000 = B\r<BR>\n" );
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document.write( "But I don't know where to go from there.<BR>\n" );
document.write( "Any help would be appreciated, Thanks!<BR>\n" );
document.write( "Sandy </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #10392 by </B><A HREF=/tutors/aboutme.mpl?userid=venugopalramana><B>venugopalramana(3286)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=venugopalramana><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.geocities.com/venugopalramana/FREE_MATHS_ASSISTANCE.html valign=middle><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=10392\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> SEE MY COMMENTS BELOW<BR>\n" );
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document.write( "Here is my problem: <BR>\n" );
document.write( "A father and his two sons bought a drug store for $320,000. If the father<BR>\n" );
document.write( "invested twice as much as the older son, and the older son invested<BR>\n" );
document.write( "$45,000 less than twice the younger son, how much did the father and <BR>\n" );
document.write( "his sons each invest? <BR>\n" );
document.write( "This needs to be solved as a linear equation.<BR>\n" );
document.write( "The answer is: younger son, $65,000; older son, $85,000; father $170,000 <BR>\n" );
document.write( "I started with:<BR>\n" );
document.write( "Father = A, older son = B and younger son = C..........GOOD...BUT THERE IS A BETTER OPTION...THE LESS THE NUMBER OF UNKNOWNS THE BETTER..I SHALL SHOW IT SEPERATELY...FIRST LET US GO BY YOUR THINKING<BR>\n" );
document.write( "A + B + C = 320,000....VERY GOOD....BETTER NAME IT AS EQN.I<BR>\n" );
document.write( "2B = A........VERY GOOD ......BETTER NAME IT AS EQN.II<BR>\n" );
document.write( "2C - 45,000 = B .....EXCELLENT.....BETTER NAME IT AS EQN.III<BR>\n" );
document.write( "But I don't know where to go from there.....AS USUAL YOU ARE AT THE END OF THE TUNNEL ,BUT NOT ABLE TO SEE THE LIGHT...THINK IT OUT THIS WAY..WE HAVE 3 UNKNOWNS..A,B,C....SO WE NEED 3 INDEPENDENT RELATIONS TO FIND THEM...AND WE HAVE 3 EQNS.NUMBERED ABOVE...WE TRY TO MAKE 3 TO 2 AND FROM 2 TO 1 UNKNOWNS.<BR>\n" );
document.write( "EQN.I HAS ALL 3 UNKNOWNS..SO LET US KEEP IT OUT FOR SOME TIME...EQNS.II AND III HAVE ONLY 2 UNKNOWNS...SO LET US TAKE THEM...FROM EQN.II,WE HAVE A=2B............................EQN.IV<BR>\n" );
document.write( "SO LET US TRY TO FIND C ALSO INTERMS OF B FROM EQN.III.<BR>\n" );
document.write( "2C-45000=B<BR>\n" );
document.write( "2C=(B+45000)<BR>\n" );
document.write( "C=(B+45000)/2.................EQN.V<BR>\n" );
document.write( "NOW SUSTITUTE EQNS.IV AND V IN EQN.I<BR>\n" );
document.write( "2B+B+(B+45000)/2=320000<BR>\n" );
document.write( "3B+(B+45000)/2=320000<BR>\n" );
document.write( "MULTIPLY THROUGH OUT WITH 2<BR>\n" );
document.write( " 6B+B+45000=640000<BR>\n" );
document.write( "7B=640000-45000=595000<BR>\n" );
document.write( "B=595000/7=85000<BR>\n" );
document.write( "A=2B=170000<BR>\n" );
document.write( "C=(B+45000)/2=65000<BR>\n" );
document.write( "Any help would be appreciated, Thanks!.....<BR>\n" );
document.write( "Sandy<BR>\n" );
document.write( "NOW ON TO BETTER PRACTICE...TAKE ANY CONVENIENT UNKNOWN AS X ..HERE YOUNGER SON IS THE CONVENIENT CHOICE SO LET YOUNGER SON'S INVESTMENT=X<BR>\n" );
document.write( "TWICE THIS =2X<BR>\n" );
document.write( "LESS 45OOO IS =2X-45000=OLDER SON'S INVESTMENT<BR>\n" );
document.write( "TWICE THIS =2(2X-45000)=4X-90000=FATHER'S INVESTMENT<BR>\n" );
document.write( "BUT TOTAL INVESTMENT IS 3200000<BR>\n" );
document.write( "SO X+2X-45000+4X-90000=320000<BR>\n" );
document.write( "7X=320000+90000+45000=455000<BR>\n" );
document.write( "X=65000...ETC.....<BR>\n" );
document.write( " </SPAN>\n" );
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