document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=473104>Question 473104</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two numbers have a sum of 50.  If the second number is 2 more than 3 times the first number, what are the 2 numbers?  <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #324490 by </B><A HREF=/tutors/aboutme.mpl?userid=karaoz><B>karaoz(32)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=karaoz><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=karaoz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=324490\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br> The unknown values are two numbers. <BR>\n" );
document.write( "Let's name them m and n.<BR>\n" );
document.write( "<br>Next, translate the relevant information into algebraic statements using m and n.<BR>\n" );
document.write( "From the first sentence we know that m + n = 50.<BR>\n" );
document.write( "From the second sentence we know that n = 3m + 2 and we know that they want us to to find the values for m and n.<BR>\n" );
document.write( "<br>Writing only algebraic statements now, we have:<BR>\n" );
document.write( "m + n = 50<BR>\n" );
document.write( "n = 3m + 2,<BR>\n" );
document.write( "which is the system of 2 equations with 2 unknowns.<BR>\n" );
document.write( "<br>We can use the second equation to substitute for n in the first equation.<BR>\n" );
document.write( "This way we will get new equation that has only one variable in it.<BR>\n" );
document.write( "m + (3m + 2) = 50<BR>\n" );
document.write( "Simplifying the above, we have:<BR>\n" );
document.write( "4m + 2 = 50.<BR>\n" );
document.write( "Taking away 2 from both sides of the equation, we get:<BR>\n" );
document.write( "4m + 2 - 2 = 50 - 2<BR>\n" );
document.write( "Simplifying,<BR>\n" );
document.write( "4m = 48<BR>\n" );
document.write( "Dividing both sides of the equation by 4:<BR>\n" );
document.write( "m = 12.<BR>\n" );
document.write( "We now know the first number m.<br><BR>\n" );
document.write( "We can find the second number from any of the two original equations while using the obtained value for m.<BR>\n" );
document.write( "Using the second equation will be easier:<BR>\n" );
document.write( "n = 3m + 2<BR>\n" );
document.write( "n = 3(12) + 2<BR>\n" );
document.write( "n = 36 + 2<BR>\n" );
document.write( "n = 38.<br>\r<BR>\n" );
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document.write( "<i> The numbers are 12 and 38.</i><BR>\n" );
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