document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=211233>Question 211233</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/9780073533490/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Professor williamson counts his midterm as 2/3 of the grade and his final as 1/3 of the grade. Wendy scored only 48 on the midterm what range of scores on the final exam would put wendy's average between 70-90 inclusive?\r<BR>\n" );
document.write( "\n" );
document.write( "I tried this 48 + x = 79<BR>\n" );
document.write( "                  x = 79-48<BR>\n" );
document.write( "                  x = 28 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #159603 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=159603\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> midterm counts as 2/3 of the grade.<BR>\n" );
document.write( "final counts as 1/3 of the grade.<BR>\n" );
document.write( "----<BR>\n" );
document.write( "wendy scores only 48 on the midterm.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "her final score will be 2/3 * 48 + 1/3 * x<BR>\n" );
document.write( "where x is her grade on the final.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "let y = final grade<BR>\n" );
document.write( "equation becomes:<BR>\n" );
document.write( "y = 2/3 * 48 + 1/3 * x<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "simplifying this equation, we get:<BR>\n" );
document.write( "y = 32 + x/3<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "multiply both sides of this equation by 3 to get:<BR>\n" );
document.write( "3y = 96 + x<BR>\n" );
document.write( "solve for x to get:<BR>\n" );
document.write( "x = 3y - 96<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "she needs to get a final grade that is between 70 and 79.<BR>\n" );
document.write( "remember that x is what she needs to get on the final exam and y is what she needs to get as a final grade.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "let's find out what she needs for 70 first.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "let y = 70<BR>\n" );
document.write( "equation of x = 3*y - 96 becomes:<BR>\n" );
document.write( "x = 3 * 70 - 96<BR>\n" );
document.write( "this becomes:<BR>\n" );
document.write( "x = 210 - 96 = 114<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "now let's find out what she needs for 79.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "let y = 79<BR>\n" );
document.write( "equation of x = 3*y - 96 becomes:<BR>\n" );
document.write( "x = 3 * 79 - 96<BR>\n" );
document.write( "this becomes:<BR>\n" );
document.write( "x = 237 - 96 = 141<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "she would need 114 on the final exam to get a final score of 70.<BR>\n" );
document.write( "she would need 141 on the final exam to get a final score of 79.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "let's plug these answers in the original formula to see if they make sense.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "she got 48 on the midterm.<BR>\n" );
document.write( "she gets 114 on the final.<BR>\n" );
document.write( "2/3 * 48 + 1/3 * 114 = 32 + 38 = 70 final grade<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "she got 48 on the midterm.<BR>\n" );
document.write( "she gets 141 on the final.<BR>\n" );
document.write( "2/3 * 48 + 1/3 * 141 = 32 + 47 = 79 final grade<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "answer is:<BR>\n" );
document.write( "she needs to get between 114 and 141 on the final exam in order to get a final grade between 70 and 79.<BR>\n" );
document.write( "----- </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );