document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1173955>Question 1173955</A>: <I><SPAN STYLE=\"word-break: break-all;\"> squares, circles and pentagons in the ratio 3:4:1 respectively.<BR>\n" );
document.write( "The shapes are either made of wood or plastic. <BR>\n" );
document.write( "The ratio of wood squares to plastic squares is 3:2.<BR>\n" );
document.write( "25% of the circles are wood.<BR>\n" );
document.write( "2/3 of the pentagons are wood.<BR>\n" );
document.write( "If there are 27 wood squares, how many plastic shapes are there? <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 #799289 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=799289\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Let's label each sentence as fact 1 through fact 6<ul><li>Fact 1) squares, circles and pentagons in the ratio 3:4:1 respectively.</li><li>Fact 2) The shapes are either made of wood or plastic.</li><li>Fact 3) The ratio of wood squares to plastic squares is 3:2.</li><li>Fact 4) 25% of the circles are wood.</li><li>Fact 5) 2/3 of the pentagons are wood.</li><li>Fact 6) There are 27 wood squares</li></ul>From fact 3 and fact 6, we can say<BR>\n" );
document.write( "(27 wood squares)/(x plastic squares) = 3/2<BR>\n" );
document.write( "27/x = 3/2<BR>\n" );
document.write( "27*2 = x*3<BR>\n" );
document.write( "54 = 3x<BR>\n" );
document.write( "3x = 54<BR>\n" );
document.write( "x = 54/3<BR>\n" );
document.write( "x = 18<BR>\n" );
document.write( "There are 18 plastic squares.<BR>\n" );
document.write( "Let A = 18 since we'll use it later.<BR>\n" );
document.write( "There are 27+18 = 45 squares overall.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Let y be some positive whole number.<BR>\n" );
document.write( "The ratio 3:4:1 is equivalent to 3y:4y:1y when we multiply both parts by y.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "This new ratio says that we have 3y squares, 4y circles, and 1y pentagons. Earlier we found that we have 45 squares. <BR>\n" );
document.write( "So,<BR>\n" );
document.write( "3y = 45<BR>\n" );
document.write( "y = 45/3<BR>\n" );
document.write( "y = 15\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "This y value leads to<BR>\n" );
document.write( "3y = 3*15 = 45 squares<BR>\n" );
document.write( "4y = 4*15 = 60 circles<BR>\n" );
document.write( "1y = 1*15 = 15 pentagons<BR>\n" );
document.write( "The ratio 45:60:15 reduces to 3:4:1 when you divide all three parts by the GCF 15.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "25% of the circles are wood (fact 4), so <BR>\n" );
document.write( "25% of (60 circles) = 0.25*60 = 15 <BR>\n" );
document.write( "We have 15 wood circles and 60-15 = 45 plastic circles.<BR>\n" );
document.write( "Let B = 45 since we'll need it later.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Earlier we found there are 15 pentagons. Two-thirds of those pentagons are wood (fact 5), which means (2/3)*15 = 10 pentagons are wood and 15-10 = 5 pentagons are plastic. <BR>\n" );
document.write( "Let C = 5.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The values of A,B,C were aimed to collect all the plastic shape counts<BR>\n" );
document.write( "A+B+C = 18+45+5 = 68\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "There are 68 plastic shapes\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Answer:  68<BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );