document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=248028>Question 248028</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the greatest possible pair of integers such that one integer is twice the other and their sum is less than 30.<BR>\n" );
document.write( "I tried x+2x<30<BR>\n" );
document.write( "          3x<30<BR>\n" );
document.write( "           x<10<BR>\n" );
document.write( "but I know that is not correct and I can not understand what I am forgetting to do in my calculation, please help, 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 #180805 by </B><A HREF=/tutors/aboutme.mpl?userid=oberobic><B>oberobic(2304)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=oberobic><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=180805\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You have two integers, say, x and y.<BR>\n" );
document.write( "Let y = 2x, which means it is twice the value of x.<BR>\n" );
document.write( "We are told to solve x + y < 30.<BR>\n" );
document.write( "So we start with the equivalent equation:<BR>\n" );
document.write( "x + 2x = 30<BR>\n" );
document.write( "x = 10<BR>\n" );
document.write( "y = 2x = 20<BR>\n" );
document.write( ".<BR>\n" );
document.write( "So the two largest integers that solve the equivalent equation x+y = 30 are x=10 and y=20.<BR>\n" );
document.write( "BUT<BR>\n" );
document.write( "We are solving an inequality, not an equation.  So, looking back, we see that x+y = 30 is NOT an acceptable answer.  The requirement is that are x+y < 30.<BR>\n" );
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document.write( "Since we are still dealing only with integers, we can subtract 1 from x, which makes x = 9.<BR>\n" );
document.write( "Then we can find y = 2x = 18<BR>\n" );
document.write( ".<BR>\n" );
document.write( "So, our proposed answer is:<BR>\n" );
document.write( "x =9<BR>\n" );
document.write( "y = 18<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Checking our work to make sure x+y < 30...<BR>\n" );
document.write( "x + y = 9 + 18 = 27 < 30. Which is fine.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Note that there is an intuitive value in the 27 in that we subtracted 1 from x, so we subtracted 2*1 from y, or 3 in total from 30.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "A non-algebraic, brute force approach could be used with a problem like this.  Simply set up table and plug in values to find the maximum value of x + 2x that is less than 30. BUT if you have to show your algebra teacher your work, the \"brute force\" approach will not earn much, if any, credit.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Done. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );