document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1165717>Question 1165717</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Rachel and Mari is a student athlete, they have played for Manila Meet, Palarong<BR>\n" );
document.write( "Pambansa and represented our school in UAAP. So far, Rachel has won 24 out of 40<BR>\n" );
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document.write( "a. Write a rational equation for the given<BR>\n" );
document.write( "b. How many matches will Rachel have to win in a row to improve her winning percentage<BR>\n" );
document.write( "to 75 %?<BR>\n" );
document.write( "c. How many matches will Rachel have to win in a row to improve her winning percentage<BR>\n" );
document.write( "to 90%? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #790181 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=790181\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> so far rachel has won 24 out of 40.<BR>\n" );
document.write( "her winning percentage is 24 / 40 * 100 = 60%.\r<BR>\n" );
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document.write( "let y equal the percent of matches she has won.<BR>\n" );
document.write( "let x = the number of matches she has to to win.\r<BR>\n" );
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document.write( "when x = 40, the number of wins is 24 for a percentage of wins of 24/40 = .6 * 100 = 60%.\r<BR>\n" );
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document.write( "our equation will be y = x / (x + 16) * 100.\r<BR>\n" );
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document.write( "y represents the percent of games won.<BR>\n" );
document.write( "x represents the number of games won<BR>\n" );
document.write( "x + 16 represents the number of games played.<BR>\n" );
document.write( "x/(x+16) represents the ratio of games won.<BR>\n" );
document.write( "x/(x+16) represents the percent of games won.\r<BR>\n" );
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document.write( "since rachel has to win every additional match she plays, the number of wins and the number of games played increments by 1 every time x increments by 1.\r<BR>\n" );
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document.write( "when y = 60, the equation becomes:<BR>\n" );
document.write( "60 = x / (x + 16) * 100<BR>\n" );
document.write( "multiply both sides of this equation by (x + 16) to get:<BR>\n" );
document.write( "60 * (x + 16) = 100 * x<BR>\n" );
document.write( "factor the left side of this equation to get:<BR>\n" );
document.write( "60 * x + 60 * 16 = 100 * x<BR>\n" );
document.write( "subtract 60 * x from both sides of this equation to get:<BR>\n" );
document.write( "60 * 16 = 100 * x - 60 * x<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "960 = 40 * x<BR>\n" );
document.write( "solve for x to get:<BR>\n" );
document.write( "x = 960 / 40 = 24.\r<BR>\n" );
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document.write( "when x = 24, she has won 24 games out of a total of 40 games for a winning percentage of 24/40 * 100 = 60%.\r<BR>\n" );
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document.write( "when y = 75, the equation becomes:<BR>\n" );
document.write( "75 = x / (x + 16) * 100<BR>\n" );
document.write( "multiply both sides of this equation by (x + 16) to get:<BR>\n" );
document.write( "75 * (x + 16) = 100 * x<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "75 * x + 16 * 75 = 100 * x<BR>\n" );
document.write( "subtract 75 * x from both sides of the equation and simplify to get:<BR>\n" );
document.write( "1200 = 25 * x<BR>\n" );
document.write( "solve for x to get:<BR>\n" );
document.write( "x = 1200 / 25 = 48\r<BR>\n" );
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document.write( "when x = 48, she has won 48 games out of a total of 64 games for a winning percentage of 48/64 * 100 = 75%.\r<BR>\n" );
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document.write( "when y = 90, the equation becomes:<BR>\n" );
document.write( "90 = x / (x + 16) * 100<BR>\n" );
document.write( "multiply both sides of this equation by (x + 16) to get:<BR>\n" );
document.write( "90 * (x + 16) = 100 * x<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "90 * x + 1440 = 100 * x<BR>\n" );
document.write( "subtract 90 * x from both sides of the equation to get:<BR>\n" );
document.write( "1440 = 10 * x<BR>\n" );
document.write( "solve for x to get:<BR>\n" );
document.write( "x = 144\r<BR>\n" );
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document.write( "when x = 144, she has won 144 games out of 160 for a winning percentage of 144 / 160 * 100 = 90%.\r<BR>\n" );
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document.write( "the equation can be graphed.<BR>\n" );
document.write( "it looks like this:\r<BR>\n" );
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document.write( " </SPAN>\n" );
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