document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=597196>Question 597196</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sum of three numbers is 4. The first number minus the second plus 5 times the third is<BR>\n" );
document.write( "20. The third plus 5 times the first plus the second is -8. Find the numbers. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #378084 by </B><A HREF=/tutors/aboutme.mpl?userid=math-vortex><B>math-vortex(648)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math-vortex><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=math-vortex><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=378084\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hi, there--\r<BR>\n" );
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document.write( "To solve this problem, we define variables for each number. Then we create a system of three equations in three variables. Finally, we solve the system of equations to find the three numbers.<BR>\n" );
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document.write( "[I] Define the variables.\r<BR>\n" );
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document.write( "Call the first number a.<BR>\n" );
document.write( "Call the second number b.<BR>\n" );
document.write( "Call the third number c.<BR>\n" );
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document.write( "[II] Create three equations.<BR>\n" );
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document.write( "The sum of the three numbers is 4. Using algebra, we write this relationship as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bb%2Bc=4 ALIGN=MIDDLE  ALT=\"a%2Bb%2Bc=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The first number minus the second plus 5 times the third is<BR>\n" );
document.write( "20. In algebra we write this relationship as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a-b%2B5c=20 ALIGN=MIDDLE  ALT=\"a-b%2B5c=20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The third plus 5 times the first plus the second is -8. In algebra we write this relationship as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%2B5a%2Bb=-8 ALIGN=MIDDLE  ALT=\"c%2B5a%2Bb=-8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Rewrite the third equation to have the variables in alphabetical order.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5a%2Bb%2Bc=-8 ALIGN=MIDDLE  ALT=\"5a%2Bb%2Bc=-8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "[III] Solve the system of equation.<BR>\n" );
document.write( "I'll use the elimination and substitution methods here. You can also use a matrix to easily solve the system. Email me at my gmail address below if you want to see the matrix method, or repost this problem and ask for a matrix method solution.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bb%2Bc=4 ALIGN=MIDDLE  ALT=\"a%2Bb%2Bc=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a-b%2B5c=20 ALIGN=MIDDLE  ALT=\"a-b%2B5c=20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5a%2Bb%2Bc=-8 ALIGN=MIDDLE  ALT=\"5a%2Bb%2Bc=-8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Add the 1st and 2nd equations together; solve to give an equation in a and c (NOTE: b+(-b)=0.)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2a%2B6c=24%7D%7D%0D%0A.%0D%0AAdd+the+2nd+and+3rd+equations+together+to+give+another+equation+in+a+and+c.%0D%0A%7B%7B%7B6a%2B6c=12 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6a%2B6c=12 ALIGN=MIDDLE  ALT=\"6a%2B6c=12\"   DISABLED_style= \"max-width:90%; height:auto;\" > from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2a%2B6c=24 ALIGN=MIDDLE  ALT=\"2a%2B6c=24\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Solve for a.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4a=12 ALIGN=MIDDLE  ALT=\"-4a=12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=-3 ALIGN=MIDDLE  ALT=\"a=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Substitute -3 for a in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2a%2B6c=24 ALIGN=MIDDLE  ALT=\"2a%2B6c=24\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Solve for c.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28-3%29%2B6c=24 ALIGN=MIDDLE  ALT=\"2%28-3%29%2B6c=24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-6%29%2B6c=24 ALIGN=MIDDLE  ALT=\"%28-6%29%2B6c=24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6c=30 ALIGN=MIDDLE  ALT=\"6c=30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=5 ALIGN=MIDDLE  ALT=\"c=5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Substitute -3 for a and 5 for c in the first equation. Solve for b.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bb%2Bc=4 ALIGN=MIDDLE  ALT=\"a%2Bb%2Bc=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-3%29%2Bb%2B%285%29=4 ALIGN=MIDDLE  ALT=\"%28-3%29%2Bb%2B%285%29=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Bb=4 ALIGN=MIDDLE  ALT=\"2%2Bb=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=2 ALIGN=MIDDLE  ALT=\"b=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "According to our algebra, the three numbers are -3, 2, and 5.<BR>\n" );
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document.write( "[IV] Check your work.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bb%2Bc=4 ALIGN=MIDDLE  ALT=\"a%2Bb%2Bc=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-3%29%2B2%2B5=4 ALIGN=MIDDLE  ALT=\"%28-3%29%2B2%2B5=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4=4 ALIGN=MIDDLE  ALT=\"4=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Check!<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a-b%2B5c=20 ALIGN=MIDDLE  ALT=\"a-b%2B5c=20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-3%29-2%2B5%285%29=20 ALIGN=MIDDLE  ALT=\"%28-3%29-2%2B5%285%29=20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5%2B25=20 ALIGN=MIDDLE  ALT=\"-5%2B25=20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20=20 ALIGN=MIDDLE  ALT=\"20=20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Bingo!<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%2B5a%2Bb=-8 ALIGN=MIDDLE  ALT=\"c%2B5a%2Bb=-8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%29%2B5%28-3%29%2B%282%29=-8 ALIGN=MIDDLE  ALT=\"%285%29%2B5%28-3%29%2B%282%29=-8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5-15%2B2=-8 ALIGN=MIDDLE  ALT=\"5-15%2B2=-8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8=-8 ALIGN=MIDDLE  ALT=\"-8=-8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Presto!<BR>\n" );
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document.write( "That's it! Feel free to email me via gmail with any questions about the solution.<BR>\n" );
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document.write( "Ms.Figgy<BR>\n" );
document.write( "math.in.the.vortex@gmail.com<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );