Question

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?

Answer 1

Answer: Y=10

Step-by-step explanation: Y=K(x/z) if y=15, x=10 and z=4 substituting in the equation

15 =K(10/4) solving by cross multiplication of 4 and 15 and dividing their product by 10 is K =6.

If x=20, Z=6 then Y = 6(20/6) then Y = 10.

Answer 2

y=20

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.