document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=243543>Question 243543</A>: <I><SPAN STYLE=\"word-break: break-all;\"> There are two numbers with the following properties.<BR>\n" );
document.write( "1) the second number is 3 more than the first number.<BR>\n" );
document.write( "2) the product of the two numbers is 9 more than their sum.<BR>\n" );
document.write( "Which of the following represents possible values of these two numbers?<BR>\n" );
document.write( "A) -6,-3    B)-4,-1   C)-1,4   D)-3,6<BR>\n" );
document.write( "*ALSO CAN YOU PLEASE SHOW ME THE STEPS TO SOLVE THE QUESTION? 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 #178405 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=178405\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A key to simplifying word problems is to use as few unknowns as possible.  Usually this means defining two (or more) variables in terms of one unknown.<BR>\n" );
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document.write( "For example, we are told there are two numbers.  That suggests x & y.  But we also are told that y is 3 more than x, which can be shown as x+3.  So we can use this approach here.<BR>\n" );
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document.write( "The product of the two numbers is 9 more than their sum.<BR>\n" );
document.write( "x(x+3) = x + (x+3) + 9<BR>\n" );
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document.write( "Multiplying the left-hand factor, we have<BR>\n" );
document.write( "x^2 + 3x = x + (x+3) + 9<BR>\n" );
document.write( "Collecting like terms:<BR>\n" );
document.write( "x^2 + 3x = 2x + 12<BR>\n" );
document.write( "Subtracting 2x from both sides:<BR>\n" );
document.write( "x^2 + x = 12<BR>\n" );
document.write( "Subtracting 12 from both sides:<BR>\n" );
document.write( "x^2 + x - 12 = 0<BR>\n" );
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document.write( "Now we have to decide if we can factor the quadratic.  We see that 3*4 = 12 are separated by just 1. And since the 12 is negative, we use opposite signs:  -3 and +4 = 1.<BR>\n" );
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document.write( "(x-3)(x=4) = 0<BR>\n" );
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document.write( "We have two candidate solutions:  x=3 and x=-4.<BR>\n" );
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document.write( "Testing x=3.<BR>\n" );
document.write( "The consecutive terms would be 3 and 6.<BR>\n" );
document.write( "The second number is now 3 more than the first<BR>\n" );
document.write( "The product is 3*6 = 18.<BR>\n" );
document.write( "The sum is 3+6=9, which is 9 less than 18.<BR>\n" );
document.write( "So that checks.<BR>\n" );
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document.write( "Testing x = -4.<BR>\n" );
document.write( "The terms would be -4 and -1.<BR>\n" );
document.write( "The product = -4 * -1 = 4.<BR>\n" );
document.write( "The sum = -4 + -1 = -5.<BR>\n" );
document.write( "Are they 9 apart?  Yes.<BR>\n" );
document.write( "So that checks, too.<BR>\n" );
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document.write( "That means the values are:<BR>\n" );
document.write( "-4, -1<BR>\n" );
document.write( "and<BR>\n" );
document.write( "3, 6<BR>\n" );
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