document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=146803>Question 146803</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve:\r<BR>\n" );
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document.write( "One number is 11 less than a second number. Twice the second number is 52 more than 4 times the first. Find the two numbers. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #107226 by </B><A HREF=/tutors/aboutme.mpl?userid=24HoursTutor.com><B>24HoursTutor.com(40)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=24HoursTutor.com><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=107226\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let the two numbers be x and y.  Now, we understand from the first sentence that the first number which we have assumed to be x is 11 less than the second number y.  Which means that if we add eleven to the first number we will get the second number.  Thus, we get the equation as : \r<BR>\n" );
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document.write( "   x + 11 = y\r<BR>\n" );
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document.write( "Now, the second sentence tells us that twice the second number, y in our case is equal to 4 times the first number(x) and 52 more.  So we have :\r<BR>\n" );
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document.write( "   2y = 52 + 4x\r<BR>\n" );
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document.write( "Since we have an equation for y , we substitute it in this equation to get :\r<BR>\n" );
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document.write( "   2(x+11) = 52 + 4x<BR>\n" );
document.write( "   2x + 22 = 52 + 4x<BR>\n" );
document.write( "   2x - 4x = 52 -22<BR>\n" );
document.write( "      - 2x = 30<BR>\n" );
document.write( "         x = 30 / -2<BR>\n" );
document.write( "         x = -15\r<BR>\n" );
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document.write( "Now, since we have the value of x, we can get the value of y by :<BR>\n" );
document.write( "   y = x + 11<BR>\n" );
document.write( "   y = -15 + 11<BR>\n" );
document.write( "   y = -4\r<BR>\n" );
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document.write( "Ans.: The first number is -15 and the second number is -4.  You can cross check your answer by substituting the value in both the equations and seeing if they still hold true.\r<BR>\n" );
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