Direct and indirect variation help please!

Question

y varies directly as x and inversely as the square of z. y=20 when x=50 and z=5. Find y when x=3 and z=6.

Please help - the answer is 5/6 but I have no idea how to get here...I think the square is messing me up. Thanks!

Answer 1

if y varies directly as x, then y = kx

if y varies inversely as x, then y = k/x, where k is a constant

so the first sentence simply means:

y = kx/z²

you're given y = 20, x = 50, and z = 5. Substitute:

20 = k(50)/(5)²

20 = k(50)/(25)

20 = k(2)

k = 10

so your new equation is:

y = 10x/z²

now you're given x = 3 and z = 6. Plug those in the new equation

y = 10(3)/(6)²

y = 30/36

y = 5/6

hope it helps :-)