document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=472641>Question 472641</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1.	Kevin and Karen are brother and sister. Kevin has twice as many sisters as he has brothers. Karen has the same number of brothers as sisters. <BR>\n" );
document.write( "a.	Set up a system of equations to model this situation. How did you figure out what each equation would be? Let d be the number of daughters that Kevin and Karen’s parents have, and s be the number of sons that Kevin and Karen’s parents have.<BR>\n" );
document.write( "b.	Solve the system of equations, showing all your work. <BR>\n" );
document.write( "c.	How many sisters does Kevin have?<BR>\n" );
document.write( "d.	How many sisters does Karen have?<BR>\n" );
document.write( "e.	How many brothers does Kevin have?<BR>\n" );
document.write( "f.	How many brothers does Karen have?<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #324074 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=324074\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> kevin and karen are brother and sister.<BR>\n" );
document.write( "d = number of daughters in the family.<BR>\n" );
document.write( "s = number of sons in the family.<BR>\n" );
document.write( "the number of brothers that kevin has is s-1.<BR>\n" );
document.write( "the number of sisters that kevin has is d.<BR>\n" );
document.write( "the number of brothers that karen has is s.<BR>\n" );
document.write( "the number of sisters that karen has is d-1.<BR>\n" );
document.write( "kevin has twice as many sisters as he has brothers.<BR>\n" );
document.write( "this means that d = 2 * (s-1).<BR>\n" );
document.write( "karen has the same number of brothers as sisters.<BR>\n" );
document.write( "this means that d-1 = s.<BR>\n" );
document.write( "the 2 equations we have to work with are:<BR>\n" );
document.write( "d = 2 * (s-1) (first equation)<BR>\n" );
document.write( "d-1 = s (second equation)<BR>\n" );
document.write( "that's our system of equations.<BR>\n" );
document.write( "we need to solve for either d or s and, from that, we should be able its partner.<BR>\n" );
document.write( "we start with the second equation of d-1 = s.<BR>\n" );
document.write( "this is the same as s = d-1.<BR>\n" );
document.write( "we can substitute for s in the first equation to get:<BR>\n" );
document.write( "d = 2 * (s-1) becomes:<BR>\n" );
document.write( "d = 2 * ((d-1)-1) which becomes:<BR>\n" );
document.write( "d = 2 * (d-2) which becomes:<BR>\n" );
document.write( "d = 2*d - 4<BR>\n" );
document.write( "subtract d from both sides of this equation and add 4 to both sides of this equation to get:<BR>\n" );
document.write( "d = 4<BR>\n" );
document.write( "if this is right, the number of daughters is 4.<BR>\n" );
document.write( "we can now substitute in the second equation to solve for s.<BR>\n" );
document.write( "the second equation is:<BR>\n" );
document.write( "d-1 = s<BR>\n" );
document.write( "since d = 4, this means that s equals 3.<BR>\n" );
document.write( "we now have:<BR>\n" );
document.write( "d = 4 (number of daughters)<BR>\n" );
document.write( "s = 3 (number of sons)<BR>\n" );
document.write( "we need to confirm these numbers are good.<BR>\n" );
document.write( "the opening statement of the problem is:<BR>\n" );
document.write( "1.	Kevin and Karen are brother and sister. Kevin has twice as many sisters as he has brothers. Karen has the same number of brothers as sisters. <BR>\n" );
document.write( "we know that kevin has s-1 brothers.<BR>\n" );
document.write( "this means that kevin has 3 - 1 brothers which is equal to 2.<BR>\n" );
document.write( "we know that kevin has d sisters.<BR>\n" );
document.write( "this means that kevin has 4 sisters.<BR>\n" );
document.write( "4 sisters is twice as many as 2 brothers, so the first part of the opening statement is confirmed as correct.<BR>\n" );
document.write( "karen has the same number of brothers and sisters.<BR>\n" );
document.write( "karen has 2 brothers which is equal to 3.<BR>\n" );
document.write( "karen has d-1 sisters which is equal to 4 - 1 = 3<BR>\n" );
document.write( "3 brothers is equal to 3 sisters, so the second part of the opening statement is confirmed as correct.<BR>\n" );
document.write( "answers to the questions are:<BR>\n" );
document.write( "c. How many sisters does Kevin have? (4)<BR>\n" );
document.write( "d. How many sisters does Karen have? (3)<BR>\n" );
document.write( "e. How many brothers does Kevin have? (2)<BR>\n" );
document.write( "f. How many brothers does Karen have? (3)\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );