document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=738978>Question 738978</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine two whole numbers such that the first number increased by triple the second number is 24.<BR>\n" );
document.write( "If the first number is squared and decreased by five times itself, the result is 13 less than the second number.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #451016 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.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/cgi-bin/show-face.mpl?user=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=451016\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let the two numbers be a & b, write an equation for each statement:<BR>\n" );
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document.write( "Determine two whole numbers such that the first number increased by triple the second number is 24.<BR>\n" );
document.write( "a + 3b = 24<BR>\n" );
document.write( "3b = (24-a)<BR>\n" );
document.write( "divide by 3<BR>\n" );
document.write( "b = (8 - a/3); use this form for substitution<BR>\n" );
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document.write( "If the first number is squared and decreased by five times itself, the result is 13 less than the second number.<BR>\n" );
document.write( "a^2 - 5a = b - 13<BR>\n" );
document.write( "Replace b with (8 - a/3)<BR>\n" );
document.write( "a^2 - 5a = 8 - a/3 - 13<BR>\n" );
document.write( "a^2 - 5a = - a/3 - 5<BR>\n" );
document.write( "mult by 3 to get rid of the denominator<BR>\n" );
document.write( "3a^2 - 15a = -a - 15<BR>\n" );
document.write( "Combine as a quadratic equation on the left<BR>\n" );
document.write( "3a^2 - 15a + a + 15 = 0<BR>\n" );
document.write( "3a^2 - 14a + 15 = 0<BR>\n" );
document.write( "factors to<BR>\n" );
document.write( "(3a-5)(a-3) = 0<BR>\n" );
document.write( "only integer solution<BR>\n" );
document.write( "a = 3<BR>\n" );
document.write( "find b<BR>\n" );
document.write( "b = 8  - 3/3<BR>\n" );
document.write( "b = 7<BR>\n" );
document.write( ";<BR>\n" );
document.write( ";<BR>\n" );
document.write( "See if that works in the given statements<BR>\n" );
document.write( "\"the first number increased by triple the second number is 24.\"<BR>\n" );
document.write( "3 + 3(7) = 24<BR>\n" );
document.write( "\"first number is squared and decreased by five times itself, the result is 13  less than the second number.\"<BR>\n" );
document.write( "3^2 - 5(3) = 7 - 13<BR>\n" );
document.write( "9 - 15 = -6   <BR>\n" );
document.write( "  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );