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If x/y = 3/4, y/z = 2/3, and z/w = 5/8, what is (x + y + w)/w?

 May 17, 2020
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x/y  =  3/4     --->     4x  =  3y               (cross-multiplying)

y/z  =  2/3     --->     3y  =  2z

z/w  =  5/8    --->     8z  =  5w

 

What is  (x + y + w) / w?

 

Notice that there is no z is the question.

This means that we should rewrite each of the variables in the question in terms of z; then all the z-terms will cancel out.

 

Since  8z  =  5w     --->     w  =  (8/5)z

Since  3y  =  2z      --->     y  =  (2/3)z

Since  4x  =  3y  and  3y  =  2z,  4x  =  2z     --->     x  =  (1/2)z

 

(x + y + w) / w     --->    [ (1/2)z + (2/3)z + (8/5)z ]  /  [ (8/5)z ]

The z's will cancel     --->     [ 1/2 + 2/3 + 8/5 ] / [ 8/5 ]

                                  --->     83/30  /  8/5

                                  --->     83 / 48

 May 17, 2020

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