document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=165315>Question 165315</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Word Problems Define all variables Must set up equations and solve choosing best method.  THIS QUESTION IS ABOUT USING 3 VARIABLE EQUATIONS. <BR>\n" );
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document.write( "The sum of three numbers is 18.  The third number is four times the second, and the second number is 6 more than the first. Find the numbers. \r<BR>\n" );
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document.write( "I got the answer using guess and check, but have no clue about how to write the equation.\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 #121867 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=121867\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Follow the directions given in the problem description:<BR>\n" );
document.write( "First, assign variables to the three unknowns:<BR>\n" );
document.write( "Let a = 1st number.<BR>\n" );
document.write( "Let b = 2nd number.<BR>\n" );
document.write( "Let c = 3rd number.<BR>\n" );
document.write( "From the problem description, you can write:<BR>\n" );
document.write( "1) a+b+c = 18 \"The sum of three numbers is 18\".<BR>\n" );
document.write( "2) c = 4*b \"The third number (c) is four times the second (4*b)\"<BR>\n" );
document.write( "3) b = a+6 \"...the second number (b) is 6 more than the first (a+6)\"<BR>\n" );
document.write( "So now you have three equations with three unknowns.<BR>\n" );
document.write( "Substitute the second equation (c = 4*b) into the first equation to get:<BR>\n" );
document.write( "a+b+(4*b) = 18 Now rewrite the third equation as a = b-6 and substitute into the first equation to get:<BR>\n" );
document.write( "(b-6)+b+4*b = 18 So now you have one equation with one unknown (b) and you can solve this for b.<BR>\n" );
document.write( "b-6+b+4*b = 18 Combine like-terms:<BR>\n" );
document.write( "6b-6 = 18 Add 6 to both sides.<BR>\n" );
document.write( "6b = 24 Divide both sides by 6.<BR>\n" );
document.write( "b = 4 <BR>\n" );
document.write( "From equation 2) you can find c.<BR>\n" );
document.write( "c = 4*b<BR>\n" );
document.write( "c = 4*4<BR>\n" );
document.write( "c = 16<BR>\n" );
document.write( "From the re-written equation equation 3, you can find a:<BR>\n" );
document.write( "a = b-6<BR>\n" );
document.write( "a = 4-6<BR>\n" );
document.write( "a = -2<BR>\n" );
document.write( "The three numbers are: -2, 4, 16<BR>\n" );
document.write( "Check:<BR>\n" );
document.write( "a+b+c = 18<BR>\n" );
document.write( "(-2)+4+16 = (-2)+20 = 18. </SPAN>\n" );
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