document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=339182>Question 339182</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need to find the system of linear equations. It has to be two equations with two variables each. \r<BR>\n" );
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document.write( "On the first day of school, the percentage of boys in a particular class is 60%. During the school year, six girls move away, and are replaced in the class by six boys. This makes the class roster 75% boys. Find the number of boys and girls in the class on the first day of school. \r<BR>\n" );
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document.write( "The teacher has given this as a hint:<BR>\n" );
document.write( "1. Let x = # of boys on the first day. Let y = # of girls on the first day. <BR>\n" );
document.write( "2. Answer the question: In terms of x and y, how many boys and girls total on the first day?<BR>\n" );
document.write( "3. Answer the question: Using the answer to # 2, what is 60% of this total.<BR>\n" );
document.write( "4. The given info says x = answer to # 3.<BR>\n" );
document.write( "That will give you your first equation.<BR>\n" );
document.write( "For the second equation<BR>\n" );
document.write( "5. How do you increase x (the # of boys) by 6?<BR>\n" );
document.write( "6. Repeat #2 and #3 but with 75%.<BR>\n" );
document.write( "7. Set your answer from # 6 equal to your answer to #5.\r<BR>\n" );
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document.write( "I know how many boys and girls there were, but even with the hint, I cannot figure out what the equations are supposed to be. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #243178 by </B><A HREF=/tutors/aboutme.mpl?userid=mananth><B>mananth(16946)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mananth><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=mananth><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=243178\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let boys be x<BR>\n" );
document.write( "girls be y<BR>\n" );
document.write( "..<BR>\n" );
document.write( "total students = x+y<BR>\n" );
document.write( "..<BR>\n" );
document.write( "60 % are boys<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Number of boys = 0.6(x+y)<BR>\n" );
document.write( "Number of girls = 0.4(x+y)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "When you add 6 boys to the class<BR>\n" );
document.write( "The number of boys = 0.6(x+y)+6<BR>\n" );
document.write( "..<BR>\n" );
document.write( "The total remains the same.(x+y)<BR>\n" );
document.write( "The boys increases to 75% of total = 0.75(x+y)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "0.6(x+y)+6=0.75(x+y)<BR>\n" );
document.write( "0.6x+0.6y+6 = 0.75x+0.75y<BR>\n" );
document.write( "add -0.6x and -0.6y to both sides<BR>\n" );
document.write( "0.6x-0.6x+0.6y-0.6y+6 = 0.75x+0.75y-0.6x-0.6y<BR>\n" );
document.write( "6 = 0.15x+0.15y<BR>\n" );
document.write( "6=0.15(x+y)<BR>\n" );
document.write( "divide by 0.15<BR>\n" );
document.write( "6/0.15 = 0.15/0.15 * (x+y)<BR>\n" );
document.write( "x+y= 40<BR>\n" );
document.write( "..<BR>\n" );
document.write( "on the first day 60% were boys<BR>\n" );
document.write( "60% of 40 are boys<BR>\n" );
document.write( "0.6 * 40 = 24 boys.<BR>\n" );
document.write( "..<BR>\n" );
document.write( "the balance 16 were girls on the first day.<BR>\n" );
document.write( "..<BR>\n" );
document.write( "CHECK<BR>\n" );
document.write( "add 6 +24 = 30<BR>\n" );
document.write( "30/40 = 3/4 = 75% </SPAN>\n" );
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