The quantity y varies directly as x and inversely as zWhen x is 10 and z is 4, y is 15What is y when x is 20 and z is 6?

y=20

Step-by-step explanation:

If y varies directly as x, we know that if x increases, y will increase in the same proportion.

If y varies inversely as z, we know that if z increases, z will decrease in the same proportion.

So, when x=10 and z=4, we have y=15.

Then, x increased to 20, so we make the proportion:

old_x/new_x = old_y/new_y

10/20 = 15/new_y

new_y = 20*15/10 = 30

The z value increased from 4 to 6, and y and z are inversely related, so:

(for that operation, our old_y will be 30)

old_z/new_z = new_y/old_y

4/6 = new_y/30

new_y = 30*4/6 = 20

So the value of y for x=20 and z=6 is y=20.

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