document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1176836>Question 1176836</A>: <I><SPAN STYLE=\"word-break: break-all;\"> . Find four rational numbers such that the product of the first, third, and fourth numbers is --6. The second number is 3 less than the first number, the third is 2 less than the second, and the fourth is 2 less than the third </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #804679 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=804679\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "You can ignore one of the responses you have received, since it answers a different question than the one that is asked.<br><BR>\n" );
document.write( "I would advise you also to ignore most of the response from the other tutor, who takes 20-30 steps to start with four unknowns and four equations to end up with a single equation in one unknown.  That might be good exercise in algebra, but it is a huge waste of time.<br><BR>\n" );
document.write( "Take the time (you don't need much) to set up the problem using a single variable:<br><BR>\n" );
document.write( "1st number: x<BR>\n" );
document.write( "2nd number: x-3  (3 less than the 1st)<BR>\n" );
document.write( "3rd number: x-5  (2 less than the 2nd)<BR>\n" );
document.write( "4th number: x-7  (2 less than the 3rd)<br><BR>\n" );
document.write( "Given that the product of the 1st, 3rd, and 4th is -6, we have<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28x-5%29%28x-7%29+=+-6 ALIGN=MIDDLE  ALT=\"x%28x-5%29%28x-7%29+=+-6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Solving this algebraically means finding the roots of a cubic equation, which is a lengthy process.  Or you could finish solving the problem using a graphing calculator.<br><BR>\n" );
document.write( "But, assuming a solution is to be obtained without a calculator, I would solve the problem from here using logical reasoning and some simple calculations.<br><BR>\n" );
document.write( "The equation says the product of x, x-5, and x-7 is a negative number.  Simple analysis shows that the product is negative for values of x less than 0, or between 5 and 7.  Negative answers are far less likely, so we can look for an answer between 5 and 7.<br><BR>\n" );
document.write( "Then, since the product is EXACTLY -6, it is very likely that the factors x, x-5, and x-7 are all whole numbers.  So we try x=6 and find x(x-5)(x-7) = 6(1)(-1) = -6, as we wanted.<br><BR>\n" );
document.write( "ANSWERS:<BR>\n" );
document.write( "1st number = x = 6<BR>\n" );
document.write( "2nd number = x-3 = 3<BR>\n" );
document.write( "3rd number = x-5 = 1<BR>\n" );
document.write( "4th number = x-7 = -1<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );