document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=774420>Question 774420</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Maria's age is M. Pat's age is M+3. Five years ago, the product of their ages was 70. How old is Maria now </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #472243 by </B><A HREF=/tutors/aboutme.mpl?userid=DrBeeee><B>DrBeeee(684)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=DrBeeee><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=472243\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This is a little tricky involving a quadratic. Can you factor a quadratic?<BR>\n" );
document.write( "Let m = Maria's current age<BR>\n" );
document.write( "Let p = Pat's current age<BR>\n" );
document.write( "Then we have<BR>\n" );
document.write( "(1) p = m +3 and<BR>\n" );
document.write( "(2) (m-5)*(p-5) = 70<BR>\n" );
document.write( "Now put (1) into (2) to get<BR>\n" );
document.write( "(3) (m-5)*(m+3-5) = 70 or<BR>\n" );
document.write( "(4) (m-5)*(m-2) = 70 or <BR>\n" );
document.write( "(5) m^2 -5m - 2m + 10 = 70 or<BR>\n" );
document.write( "(6) m^2 -7m -60 = 0 which factors to<BR>\n" );
document.write( "(7) (m-12)*(m+5) = 0<BR>\n" );
document.write( "Select the positive root to get<BR>\n" );
document.write( "(8) m = 12<BR>\n" );
document.write( "Then <BR>\n" );
document.write( "(9) p = 15<BR>\n" );
document.write( "Is ((12-5)*(15-5) = 70)?<BR>\n" );
document.write( "Is (7*10 = 70)?<BR>\n" );
document.write( "Is (70 = 70)? Yes<BR>\n" );
document.write( "Answer: Maria is currently 12 years of age. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );