Modeling using variation

Question

y varies directly as x and inversely as the square of z. y = 40 when x = 36 and z = 3. Find y when x = 3 and z = 9.

Answer 1

"y varies directly as x" means y = kx (where "k" is a constant called the constant of variation)

"y varies inversely as the square of z" means y = k/z²

So since both are true: y = kx/z²

If y = 40 when x = 36 and z = 3 then we can plug those values of x, y, and z into "y = kx/z²" and solve for "k":

y = kx/z²

40 = k(36)/(3²)

40 = 36k/9

40 = 4k

k = 10

So our equation becomes: y = 10x/z²

Now, plug in x = 3 and z = 9 to find out what "y" is.