document.write( "Question 1203833: 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. \n" ); document.write( "

Algebra.Com's Answer #839685 by greenestamps(13200) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( "Type everything in your post using your keyboard. The format you use is extremely awkward.

\n" ); document.write( "And I won't try to guess how \"dfrac\" is different from \"frac\"....

\n" ); document.write( "(1) $\"x%2Fy=4%2F5\"$
\n" ); document.write( "(2) $\"y%2Fz=2%2F5\"$
\n" ); document.write( "(3) $\"z%2Fw=6%2F11\"$

\n" ); document.write( "Find $\"%28x%2By%2Bw%29%2Fz\"$

\n" ); document.write( "Method (perhaps not the easiest -- but the most straightforward): express y, z, and w in terms of x.

\n" ); document.write( " $\"x%2Fy=4%2F5\"$
\n" ); document.write( " $\"4y=5x\"$
\n" ); document.write( " $\"y=%285%2F4%29x\"$

\n" ); document.write( " $\"y%2Fz=2%2F5\"$
\n" ); document.write( " $\"2z=5y=5%285%2F4%29x=%2825%2F4%29x\"$
\n" ); document.write( " $\"z=%2825%2F8%29x\"$

\n" ); document.write( " $\"z%2Fw=6%2F11\"$
\n" ); document.write( " $\"6w=11z=11%2825%2F8%29x=%28275%2F8%29x\"$
\n" ); document.write( " $\"w=%28275%2F48%29x\"$

\n" ); document.write( "

\n" ); document.write( "ANSWER: 383/150

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