document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=351406>Question 351406</A>: <I><SPAN STYLE=\"word-break: break-all;\">  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #251095 by </B><A HREF=/tutors/aboutme.mpl?userid=NRobinson><B>NRobinson(4)</B></A><img src=\"/images/stars/iconNewId_16x16.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=NRobinson><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=251095\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Q:The sum of two numbers is 38 and their difference is 26 more than the smaller one.  What are the two numbers?\r<BR>\n" );
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document.write( "A: You will want to translate the english version of this problem into algebra. Start with the first part of the first sentence: The sum of two numbers is 38.  \r<BR>\n" );
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document.write( "We know that SUM is ADDITION, so this meas two numbers added together equal (IS) 38.  So if the smaller number is x and the larger is y, then<BR>\n" );
document.write( " x + y = 38.\r<BR>\n" );
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document.write( "Now, the second part of the sentence, their difference is 26 more than the smaller one.  The DIFFERENCE means subtraction.  We subtract the two unknowns, y - x since x was the smaller.  This is equal to 26 more than the smaller.  MORE THAN means addition (x + 26).  So now we can build a second equation, <BR>\n" );
document.write( "y - x = x + 26.\r<BR>\n" );
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document.write( "Depending on what level of mathematics you are in you can solve using two variables or substituting 38-x for y in the second equation and then using just one equation and one variable.  \r<BR>\n" );
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document.write( "x + y = 38 & y - x = x + 26:list both equations<BR>\n" );
document.write( "y = 38 - x & y = 2x + 26: solve for y <BR>\n" );
document.write( "38 - x = 2x + 26:substitute for y since both equations are equal to y<BR>\n" );
document.write( "12 = 3x: subtract 26 from both sides and add x to both sides<BR>\n" );
document.write( "4 = x:divide by 3<BR>\n" );
document.write( "y = 38 - x :go back to your first equation<BR>\n" );
document.write( "y = 38 - 4 :substitute x=4<BR>\n" );
document.write( "y = 34 :subtracct\r<BR>\n" );
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document.write( "Double check: y - x = x + 26<BR>\n" );
document.write( "y = 34, x = 4<BR>\n" );
document.write( "34 - 4 ?=? 4 + 26<BR>\n" );
document.write( "30 = 30\r<BR>\n" );
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document.write( "So the correct solution are the numbers 4 and 34 just as you had found. </SPAN>\n" );
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