document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203833>Question 1203833</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If \[\frac{x}{y} = \frac{4}{5}, \; \frac{y}{z} = \frac{2}{5}, \;\text{and} \; \frac{z}{w} = \frac{6}{11},\] what is the value of $\dfrac{x + y + w}{z}$? Express your answer as a common fraction. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #839686 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=839686\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Given equations<BR>\n" );
document.write( "x/y = 4/5<BR>\n" );
document.write( "y/z = 2/5<BR>\n" );
document.write( "z/w = 6/11\r<BR>\n" );
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document.write( "Multiply equations (1) and (2).<BR>\n" );
document.write( "We multiply left hand sides (LHS) separately. <BR>\n" );
document.write( "Do the same for the right hand sides (RHS)\r<BR>\n" );
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document.write( "LHS: (x/y) * (y/z) becomes x/z<BR>\n" );
document.write( "RHS: (4/5)*(2/5) becomes 8/25\r<BR>\n" );
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document.write( "We conclude that x/z = 8/25<BR>\n" );
document.write( "The key here is that z is the denominator.\r<BR>\n" );
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document.write( "Apply the reciprocal to both sides of equation (3) to get w/z = 11/6<BR>\n" );
document.write( "We have z in the denominator as well.\r<BR>\n" );
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document.write( "---------------------\r<BR>\n" );
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document.write( "So we have:<BR>\n" );
document.write( "x/z = 8/25<BR>\n" );
document.write( "y/z = 2/5<BR>\n" );
document.write( "w/z = 11/6<BR>\n" );
document.write( "All three equations shown above have z in the denominator.\r<BR>\n" );
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document.write( "Add them up.<BR>\n" );
document.write( "(x/z) + (y/z) + (w/z) = (8/25)+(2/5) + (11/6)<BR>\n" );
document.write( "(x + y + w)/z = (8/25)+(10/25) + (11/6)<BR>\n" );
document.write( "(x + y + w)/z = (18/25) + (11/6)<BR>\n" );
document.write( "(x + y + w)/z = (18/25)*(6/6) + (11/6)*(25/25)<BR>\n" );
document.write( "(x + y + w)/z = (108/150) + (275/150)<BR>\n" );
document.write( "(x + y + w)/z = (108+275)/150<BR>\n" );
document.write( "(x + y + w)/z = <font color=red size=4>383/150</font><BR>\n" );
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