document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1209464>Question 1209464</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If x-3 is directly proportional to the square of y and x =5 when y=2,<BR>\n" );
document.write( "What is x when y=6 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848887 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=848887\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The response from the other tutor shows a formal solution using the definition of direct variation to find the constant of proportionality and solves the problem from there.<br><BR>\n" );
document.write( "That is a good approach, and it would probably be the best approach if we needed to find the solutions for several different sets of data.<br><BR>\n" );
document.write( "But when the problem only requires us to find the answer for a single new set of data, we can use the definition of direct variation to solve the problem informally and quickly.<br><BR>\n" );
document.write( "In this problem, we are given that (x-3) is directly proportional to the square of y; and we are asked to find the value of x when y is 6, given that x is 5 when y is 2.<br><BR>\n" );
document.write( "So the y value increases by a factor of 3 (from 2 to 6); since (x-3) is directly proportional to the square of y, the value of (x-3) increases by a factor of 3^2 = 9.<br><BR>\n" );
document.write( "Originally, the value of x-3 was 5-3 = 2; 2 increased by a factor of 9 is 2*9 = 18.<br><BR>\n" );
document.write( "So the new value of x-3 is 18, which means the new value of x is 18+3 = 21.<br><BR>\n" );
document.write( "ANSWER: 21<br><BR>\n" );
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