z varies inversely with x and directly with y. When x = 6 and y = 2, z = 5. What is the value of z when x = 4 and y = 9?

20/9
5/27
135/4
60

1 Answer
John D.
Mar 20, 2017

#z = 135/4#

Explanation:

Based on the given information, we can write:

#z = k(y/x)#

Where #k# is some constant we don't know that will make this equation true. Since we know that #y# and #z# vary directly, #y# needs to go on the top of the fraction, and since #x# and #z# vary inversely, #x# needs to go on the bottom of the fraction. However, #y/x# may not be equal to #z#, so we need to put a constant #k# in there in order to scale #y/x# so that it matches up with #z#.

Now, we plug in the three values for #x, y, #and #z# which we know, in order to find out what #k# is:

#z = k(y/x)#
#5 = k(2/6)#
#15 = k#

Since #k=15#, we can now say that #z = 15(y/x)#.

To get the final answer, we now plug #x# and #y# into this equation.

#z = 15(y/x)#
#z = 15(9/4)#
#z = 135/4#

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