document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1014611>Question 1014611</A>: <I><SPAN STYLE=\"word-break: break-all;\"> write an inequality to this problem and solve: Hunter earns twice as much per week as his sister Naomi. if she makes $30 per week more than her brother Jake and the sum of their salaries is at most $330, what range can their salaries take each week? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #630915 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=630915\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> here's what i think.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "h = money hunter makes in a week.<BR>\n" );
document.write( "n = money naomi makes in a week.<BR>\n" );
document.write( "j = money jake makes in a week.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "h + n + j <= 330\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this means that the total that they all make in a week has to be less than or equal to 330.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you are given that hunter makes two times as much in a week as naomi.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the equation for this would be h = 2n.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you are given that naomi makes 30 more in a week than jake.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the equation for this is n = j + 30\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you have 3 equations to work with.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "h + n + j <= 330<BR>\n" );
document.write( "h = 2n<BR>\n" );
document.write( "n = j + 30\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you want to convert everything in terms of one of the variables if that is possible.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "since h = 2n and n = j + 30, then h = 2n becomes h = 2 * (j + 30) which becomes h = 2j + 60.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "your equation are now:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "h + n + j <= 330<BR>\n" );
document.write( "h = 2j + 60<BR>\n" );
document.write( "n = j + 30\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "in the first equation, you can replace n with j + 30 and you can replace h with 2j + 60 to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "h + n + j <= 330 becomes (2j + 60) + (j + 30) + j <= 330.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "remove parentheses to get 2j + 60 + j + 30 + j <= 330.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "combine like terms to get 4j + 90 <= 330.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "subtract 90 from both sides of this equation to get 4j <= 240.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "divide both sides of this equation by 4 to get j <= 60.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "since n = j + 30, then if j <= 60, n has to be <= 90\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "since h = 2j + 60, then if j <= 60, h has to be <= 180.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "j <= 60<BR>\n" );
document.write( "n <= 90<BR>\n" );
document.write( "h <= 180\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the maximum they can be is:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "j = 60<BR>\n" );
document.write( "n = 90<BR>\n" );
document.write( "h = 180\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the total of j + n + h would be 330.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this agrees with the problem statement so far.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the minimum they can be is calculated as follows:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the smallest one is j.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "none of them can go negative.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the smallest j can be is 0.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the smallest n can be is 30 because n = j + 30.  <BR>\n" );
document.write( "when j is equal to 0, n is equal to 30.<BR>\n" );
document.write( "if n went below 30, j would be negative, which is  not allowed.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the smallest h can be is 60 because h = 2j + 60.<BR>\n" );
document.write( "when j is equal to 0, h is equal to 60.<BR>\n" );
document.write( "if h went below 60, j would be negative, which is not allowed.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "hunters range is from 60 to 180 inclusive.<BR>\n" );
document.write( "naomi's range is from 30 to 90 inclusive.<BR>\n" );
document.write( "jake's range is from 0 to 60 inclusive.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "in interval notation, you get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "h = [60,180]<BR>\n" );
document.write( "n = [30,90]<BR>\n" );
document.write( "j = [0,60]\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "based on this, the minimum they all can be is 90 total and the maximum they all can be is 330 total.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );